Search

The nonlinear Schrödinger–Poisson equation with gravitational potential field is examined, along with its many soliton interactions and travelling wave solutions. By applying Hirota Bilinear scheme, we will give a brief study on transformation of solitons, also by Sine–Gordon expansion scheme solitary travelling wave solutions will be obtained in terms of trigonometric and hyperbolic functions. The innovative Hirota bilinear method is a powerful and standard technique, play a crucial role in producing soliton solutions as well as lump solutions. With the assistance of this method one can transformed integrable equation into Hirota bilinear form under dependent variable transformation. Soliton solutions obtained by Hirota bilinear method are significant in mathematical physics, may be superimposed in fibers. These solitons are applicable in optical communications, which enable to produce faster, richer, more secure and more flexible communication systems. Also we will investigate the gravitational potential's behaviour on soliton solutions, such as parabolic, bright, dark, anti-dark, combination and S-shaped solitons. Contour plots and three-dimensional soliton solutions are provided. These solitons are important in nonlinear processes, magnetic devices, and lasers beams because of variations in gravitational field. [ABSTRACT FROM AUTHOR]

In this work, we study the Chafee–Infante differential equation (CIDE) for various types of nonlinear waves (NW) like breather waves (BW), periodic cross-kink (PCKW), lump waves (LW), rogue waves (RW), periodic wave (PW), lump soliton (LS) with one kink, LS with two kink and periodic-cross lump waves (PCLW). The CIDE is a nonlinear evolution equation (NLEE) introduced by Nathaniel Chafee and Ettore Infante. This equation has been widely investigated in the context of pattern generation and soliton solutions, and it plays an essential role in understanding the complex nonlinear dynamics across a wide range of scientific fields. BW is a localized, non-dispersive solution to NW equations, maintaining shape and amplitude during travel. An LS is a type of solitary wave solution in NLEEs. In mathematics, RW refers to rare and unusually large solutions of NW equations. These waves have garnered significant attention due to their unpredictable and extreme nature. A PW is a type of wave that repeats its shape and behavior at regular intervals in both time and space. These waves are characterized by their periodicity, which means that they have a consistent and predictable pattern of oscillation. We’ll offer a graphical explanation of our newly discovered answers toward the conclusion. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to obtain the chirped solitons solutions of chiral nonlinear Schrödinger equation (CNLSE) with Bohm potential (CNLSE-BP) by using Jacobian elliptic function. We also obtain chirped domain walls, bright solitons, periodic solitons, hyperbolic solitons, and also some other solitary waves. The corresponding chirp that associated with these optical soliton solution has also been obtained. We also show the graphical description of our results in 3-D and 2-D. [ABSTRACT FROM AUTHOR]

Globally, infectious diseases pose a significant threat. Notable cases include influenza, Hepatitis B and HIV. COVID-19, caused by the coronavirus, has been the subject of recent discussion due to its great transmissibility. This study explores the Susceptible–Infectious–Recovered (SIR) epidemic model, explaining several analytical approaches to comprehend the nonlinear incident rates and geographic dispersion. The model investigates phenomena such as M-shaped solitons, homoclinic breather-like solitons, lump waves (LWs), lump solution (LS) with one or two kinks, rogue waves (RWs), periodic waves (PWs) and periodic cross-kink waves. These solutions aid in understanding the disease spread and informing containment strategies by identifying optimal outbreak control methods. This work studies localized wave solutions in nonlinear wave equations, known as soliton solutions including the LS. RWs are characterized by unexpectedly large amplitude and rapid profile changes, drawing attention for their erratic features. PWs exhibit periodic repetitions over time and space. Besides, some type of solitons with special waveforms are the periodic cross-kink, M-shaped and homoclinic breather-like solitons. Graphical representation visualizes the behavior of these effective waves, providing insights into virus spread in specific regions over time. SIR models help identify optimal strategies for controlling outbreaks. The work adds to our understanding of epidemic dynamics by illuminating how the movement of susceptible and infected individuals affects the spread of disease. [ABSTRACT FROM AUTHOR]

Bifurcation analysis is a powerful method for investigating the steady-state nonlinear dynamics of systems. There are software programmes that allow for the numerical continuation of steady-state solutions while the system's parameters are changed. The aim of this manuscript is to deal a mixed derivative nonlinear Schrödinger's equation (MD-NLSE), α -helix NLSE and Zoomeron model utilising the bifurcation theory technique of dynamical systems. A mathematical method called bifurcation analysis is used to examine how a system behaves when a parameter is changed. It is used to examine how the behaviour of the system changes as one or more parameters are altered and to find critical values of the parameters that cause appreciable changes in the behaviour of the system. Bifurcations are places in parameter space when the system's qualitative behaviour abruptly shifts. A system could, for instance, go from having a stable equilibrium to oscillating between two states when a parameter is increased. To investigate these changes and comprehend how the system's behaviour would alter if the parameter is further altered, bifurcation analysis is performed. An example of a phase portrait is a plot of a dynamic system's phase space, which graphically depicts the behaviour of the system. A two-dimensional depiction of the system's variables on the x and y axes is a common way to depict the phase space, which is the space of all conceivable states of the system. The paths of the system are shown as curves or lines in the phase space in a phase picture. These paths show how the system has changed over time and may be used to examine the stability and behaviour of the system. Phase portraits are often employed in the study of the behaviour of complex systems in physics, engineering, and mathematics. Numerous systems, including mechanical systems, electrical circuits, chemical processes, and biological systems, may be studied using them. Researchers can learn more about a system's dynamics and forecast how it will behave in various situations by looking at its phase picture. [ABSTRACT FROM AUTHOR]

This article uses appropriate transformations and the sub-ODE method to reveal multiwave, homoclinic breather, M-shaped rational, periodic cross rational, kink cross rational, periodic cross kink, and other soliton solutions for Einstein's vacuum field problem. Additionally, the interaction of rational solitons in the M shape with an exponential function and a double exponential form is disclosed. [ABSTRACT FROM AUTHOR]

In this paper, we study the third-order nonlinear Schrödinger equation (NLSE) and optical metamaterial (OM) with quadratic-cubic nonlinearity (OM-QCNL) to describe the properties and presence of propagating solitary waves (SW) in a fibre optic medium. We present an effective field amplitude ansatz that allows us to obtain SW using the governing model. More specifically, in the presence of all orders of dispersion and various nonlinear variables, we find SW solutions of dipole, bright, dark and other forms. The graphical representation of these waves will also be presented. [ABSTRACT FROM AUTHOR]

This paper deals with the evaluation of multiwave, homoclinic breather, M-shaped rational solitons and interaction of M-shaped rational solitons with single and double kinks for (1 + 1) -dimensional longitudinal wave equation via the logarithmic transformation and symbolic computation with ansatz functions method. We will obtain two types of M-shaped rational solitons and their dynamics are revealed in figures by choosing the distinct values of involved parameters. In addition, two forms of interaction of M-shaped rational soliton with kink wave will also be evaluated. Furthermore, we will compute kink cross-rational solutions, periodic cross-rational solutions, generalized breathers and Akhmediev breathers for governing model. The solitons behaviors via different values of parameters in the produced solutions will be analyzed. [ABSTRACT FROM AUTHOR]

This template retrieves M-shaped rational solitons and their interactions with kink waves, homoclinic breathers, multiwave, Grey-black optical solitons, periodic cross-rational solitons and kink cross-rational solitons propagation in optical fibers where self-phase modulation (SPM) is negligibly minor and therefore removed. The proposed equation contains spatio-temporal dispersions (STD), of second and third orders, to recompense for small group velocity dispersion (GVD). All new analytical solutions are found by utilizing the symbolic computation with logarithmic transformation and ansatz functions approach. Moreover, stability characteristics of all solutions are found. [ABSTRACT FROM AUTHOR]

The study of solitons including their stability, presence, validity and strength with constant increasing research is not forgettable in this era. In this research paper, we explore solitary wave solutions and dromions for Boussineq equation with the help of Hirota bilinear method (HBM) and Sine-Gordon expansion (SGE) technique. We will enlist these schemes for the study of different types of solitons by implementing HBM and SGE. We will acquire anti dark, multi-solitons, V-shaped, M-shaped, S-shaped and dark travelling wave solutions with their effects during transformations and collision. [ABSTRACT FROM AUTHOR]

This paper studies the Lax pair (LP) of the (1 + 1) -dimensional Benjamin–Bona–Mahony equation (BBBE). Based on the LP, initial solution and Darboux transformation (DT), the analytic one-soliton solution will also be obtained for BBBE. This paper contains a bunch of soliton solutions together with bright, dark, periodic, kink, rational, Weierstrass elliptic and Jacobi elliptic solutions for governing model through the newly developed sub-ODE method. The BBBE has a wide range of applications in modeling long surface gravity waves of small amplitude. In addition, we will evaluate generalized breathers, Akhmediev breathers and standard rogue wave solutions for stated model via appropriate ansatz schemes. [ABSTRACT FROM AUTHOR]

We present the Lie symmetry analysis for the famous nonlinear equation describing chains of atoms with long range interaction. We also study the conservation laws by computing the conserved density and their associated fluxes by applying the scaling invariance approach. We use the Euler and the homotopy operators for the computations of conserved density and their corresponding fluxes respectively. In addition to these, we use an auxiliary ordinary differential equation method namely sub-ODE scheme to obtain bell type, kink shape, Jacobi elliptic, hyperbolic and few other solitary wave solutions with some constraints. At the end, we discuss our results graphically in distinct dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we will study different kinds of analytical solutions for higher order nonlinear Schrödinger equation (HNLSE) under the influence of self-steeping and Raman effects, along with quintic nonlinear and septimal forms. We will obtain lump, periodic wave, periodic cross-kink, rogue wave, breathers, lump with one and two kink, periodic-cross lump and multi-wave. We will also compute the interaction, between lump periodic and kink waves, periodic cross-kink waves and other forms of solutions. To see the behaviour of these waves, for the better understanding of our solutions we will also present graphs in 3D, 2D and contour forms with constraints conditions. [ABSTRACT FROM AUTHOR]

The analytical rational solitons of the Kraenkel–Manna–Merle (KMM) system in a saturated ferromagnetic material will be explored in depth by using the symbolic computation with ansatz functions and logarithmic transformation. We investigate many systematic solutions such as lump soliton, rogue wave, lump with one kink, multiwave, periodic wave, periodic cross-kink wave and breather lump wave. We also examine M-shaped rational solution, homoclinic breather solution, M-shaped rational solution with one kink, kink-cross rational solution and M-shaped rational solution with two kink for KMM system. Additionally, we will draw graphs in different dimensions allowing analytical approaches to identify the structure of enormous waves. Furthermore, we look into the stability of a derived solutions and give a results in a tables. [ABSTRACT FROM AUTHOR]

In this article, we explore analytical rational solutions to the Peyrard Bishop DNA (PB-DNA) model such as lump soliton, kink soliton, periodic cross kink, multi wave and breather lump wave. By using ansatz transformation, we explore M-shaped rational solution for PB-DNA equation. Also, we acquire M-shaped rational solution with one kink and two kink. Furthermore, we compute kink cross rational solution, homoclinic breather solution. Additionally, two forms of interactions between the kinks waves and M-shaped rational solutions will be computed. Consequently, we study the stability of the acquired solutions and present in the form of table. We also illustrate our graphs in different dimensions such as 3D, 2D, contour and stream plots. [ABSTRACT FROM AUTHOR]

Different analytical solutions for Sasa–Satsuma model equation (SSM) in birefringent fibers are investigated in this research like rogue wave, lump, multi-wave, multiple breather solutions, periodic wave, breather lump, periodic cross kink, periodic cross lump, and lump with one and two kinks. By examining the SSM, we can compute the important relationship between the interaction between kink, lump with periodic wave and a variety of exact solutions. To see the behavior of effective waves, we illustrate the pictorial depiction for our retrieve analytical solutions. [ABSTRACT FROM AUTHOR]

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), M -shaped rational solutions, lump soliton, kink cross-rational (KCR), periodic cross-kink rational (PCKR), periodic cross-rational (PCR) solutions for the Degasperis–Procesi (DP) equation in shallow water waves through appropriate polynomial function scheme. We also compute some interactions for stated model including interaction of M -shaped soliton with one kink, interactional solution with two kinks also lump soliton with kink one and kink two solutions. Furthermore, we made suitable 3D, 2D and contour profiles via appropriate parameters. [ABSTRACT FROM AUTHOR]

This article studies diverse forms of lump-type solutions for coupled nonlinear generalized Zakharov equations (CNL-GZEs) in plasma physics through an appropriate transformation approach and bilinear equations. By utilizing the positive quadratic assumption in the bilinear equation, the lump-type solutions are derived. Similarly, by employing a single exponential transformation in the bilinear equation, the lump one-soliton solutions are derived. Furthermore, by choosing the double exponential ansatz in the bilinear equation, the lump two-soliton solutions are found. Interaction behaviors are observed and we also establish a few new solutions in various dimensions (3D and contour). Furthermore, we compute rogue-wave solutions and lump periodic solutions by employing proper hyperbolic and trigonometric functions. [ABSTRACT FROM AUTHOR]

This paper studies the soliton solutions for Embedded soliton (ES) generating model with χ 2 nonlinear susceptibility. The bright, rational, Jacobi elliptic, periodic, dark, Weierstrass, hyperbolic solitary wave solutions will be found with the aid of sub-ODE technique under certain conditions. The main objective behind the sub-ODE method is to find the wave solutions of a complex model with the help of simple and solvable ODEs called sub-ODEs. The resulting wave solutions are presented graphically for suitable values of different parameters. [ABSTRACT FROM AUTHOR]

In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons of the governing equation by means of a suitable complex envelope ansatz solution. By using the Chupin Liu's theorem (CLT) for the grey and black solitons, we evaluated new categories of combined optical soliton (COS) solutions to the IP-NLSE. The propagation behaviors for homoclinic breathers (HB), multiwaves and M-shape solitons will be analytically examined. All new analytical solutions will be found by an ansatz function scheme and suitable transformations. Multiwave solitons have been reported by using a three-waves technique. Furthermore, two kinds of interactions for M-shape soliton through exponential functions will be examined. [ABSTRACT FROM AUTHOR]

This template recoups one-soliton transformation, two and N-solitons interactions through Hirota bilinear method (HBM) for a new (3 + 1) -dimensional nonlinear Schrödinger equation (NLSE) in optical fibers. The contribution of this paper is to apply the Hirota's derivatives, generate bilinear equations and use ansatz functions approach (AFA) for the governing model. In addition to this, we compute M-shape rational solitons and their interaction with kink waves, homoclinic breathers, kink cross rational solitons and periodic cross rational solitons for governing model by utilizing the symbolic computation with logarithmic transformation and AFA. Furthermore, the multi-wave solitons and interactional phenomena are found by applying three waves approach. We construct 3D profiles for our solutions by choosing appropriate values. [ABSTRACT FROM AUTHOR]

In this paper, we examine generalized nonlinear Schrödinger equation (GNLSE) for lump, breather lump wave, rogue wave, periodic cross kink wave, lump with one kink, lump with two-kink, interaction between lump periodic and kink wave, periodic cross lump wave, periodic wave and multi-wave. Ansatz transformations will be used to study homoclinic breather, kink cross rational, M-shaped rational, periodic cross rational, M-shaped rational with one kink, M-shaped rational with two-kink, M-shaped interaction with rogue and kink and M-shaped interaction with periodic and kink. We will also study the stability of the obtained solutions. Additionally, we present three-dimensional, two-dimensional, contour, and stream plot illustrations for our graphs. [ABSTRACT FROM AUTHOR]

In this paper, we examine generalized nonlinear Schrödinger equation (GNLSE) for lump, breather lump wave, rogue wave, periodic cross kink wave, lump with one kink, lump with two kink, interaction between lump periodic and kink wave, periodic cross lump wave, periodic wave, and multiwave. Ansatz transformations will be used to study homoclinic breather, kink cross rational, M-shaped rational, periodic cross rational, M-shaped rational with one kink, M-shaped rational with two kink, M-shaped interaction with rogue and kink and M-shaped interaction with periodic and kink. We will also study the stability of the obtained solutions. Additionally, we present 3D, 2D, contour, and stream plot illustrations for our graphs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate multiple soliton interactions and other solitary wave solutions (SWS) for a perturbed nonlinear Schrödinger equation (NLSE) with negative index material having quadratic-cubic nonlinearity (NLSE-QCN). Due to its high order dispersion term, this model yields sub-picosecond impulses useful in mode-locked ring lasers. Hirota bilinear method (HBM) will be used to study soliton interaction. By controlling the parameters, we will obtain S , V , parabolic and anti-parabolic, butterfly, bright and dark shaped solitons. On the other hand, we will obtain some other solitary wave solutions with the help of Sine-Gordon expansion (SGE) scheme. [ABSTRACT FROM AUTHOR]

We explore stochastic–fractional Drinfel'd–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution. We also examine some M-shaped solutions such as the M-shaped rational solution, M-shaped rational solution with one and two kink waves. We also derive the M-shaped interaction with rogue and kink waves and the M-shaped interaction with periodic and kink waves. This model is used in mathematical physics, surface physics, plasma physics, population dynamics and applied sciences. Moreover, we also show our results graphically in different dimensions. We obtain these solutions under some constraint conditions. [ABSTRACT FROM AUTHOR]

We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots. [ABSTRACT FROM AUTHOR]

In this article, the propagation of breathers, multiwave, M-shape solitons, grey–black optical solitons, periodic cross rational (PCR) solitons, kink cross rational (KCR) solitons will be discussed under the effect of self-steepening and third-order of linear dispersion in single-mode fibers. All new analytical solutions are found by utilizing the symbolic computation with ansatz functions scheme and logarithmic transformation. Moreover two kinds of interaction of M-shape soliton with kink wave will be examined. We apply nine different approaches, namely, three-waves technique, homoclinic breather technique, M-shape solitons, single exponential form (one-kink), double exponential form (two-kink), PCR, KCR, grey optical soliton and black optical soliton for governing model. Moreover, stability characteristics of all solutions are evaluated. [ABSTRACT FROM AUTHOR]

This article retrieves, different types of solutions such as M-shaped rational solutions (M-SRSs) with one-kink, homoclinic breather, multi waves, periodic-cross-kink and kink-cross rational solutions for nonlocal Boussinesq equations. We will study the M-shaped interaction with rogue and kink, we will also acquire the M-shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions. [ABSTRACT FROM AUTHOR]

We study the propagation of M-shaped solitons and kink-periodic waves in an optical fiber medium exhibiting Kerr dispersion and quintic nonlinearity by applying the symbolic computation with ansatz functions technique and logarithmic transformation. We used seven different methods, namely, three waves technique, homoclinic breather technique, M-shaped solitons, single exponential form, double exponential form, kink cross-rational and trigonometric and hyperbolic ansatz approaches. The quintic derivative nonlinear Schrödinger equation (QD-NLSE) is applied to model for ultrashort light pulse in fibers and self-steepening processes. We compute two categories of M-shaped solitons and their dynamics are revealed in figures by appropriate values of parameters. Moreover two types of interaction of M-shaped solitons with kink wave are revealed. We attain multiwaves, kink cross-rational (KCR), Homoclinic breather, periodic cross-rational solutions (PCRs) for governing model. Finally, the stability property of all solutions is analytically studied under the finite selection of parameters. [ABSTRACT FROM AUTHOR]

In this article, we cover some soliton solutions and breathers for nonlinear Schrödinger equation with quadratic nonlinear susceptibility like that Breather lump wave solutions, Interaction between lump periodic and kink wave, lump soliton solution, Lump one kink solution, Lump two kink solution, multiwave solution, periodic cross kink solution, periodic cross lump wave solution, periodic wave solution and rogue wave solution. We also explore some rational solution such as M-shaped rational solutions, M-shaped rational solutions with one and two kink, kink cross rational solution and periodic cross rational solution. Also, we acquire homoclinic breather solution, M-shaped interaction with rogue and kink and M-shaped interaction with periodic and kink. Furthermore we also study the stability of our solutions. we also represents our solutions graphically such as 3D, 2D, contour, density plot and stream plot. [ABSTRACT FROM AUTHOR]

In this paper, we will use various ansatz transformations to obtain different kinds of optical solitons solutions for couple of nonlinear Schrödinger equations (NLSEs). We get bright, dark, bright in the dark (dipole), combined dark–bright (combo) and some other solitary wave solutions for quadratic-cubic quintic system in optical meta-materials (CQS-OM) having quadratic cubic nonlinearity along with NLSE with anti-cubic nonlinearity (AC) in an optical fiber. We also show our results graphically in various dimensions under different constraint conditions. [ABSTRACT FROM AUTHOR]

The current study deals with investigation of Einstein's vacuum field equation (EVFE) for exploring various lumps, breathers and interaction solutions via bilinear method and choosing appropriate polynomial function. In particular, we obtain lump, lump 1-strip, lump 2-strip, lump periodic, Manifold periodic, rogue wave (RW), generalized breather, Akhmediev breather, Ma breather, Kuznetsov-Ma breather and its corresponding RW solutions for ensuing model. In addition, we also made interaction among lump, periodic and kink-wave with their numeric simulation. In general relativity, the governing model play momentous part in many ambitious experiments and space missions. Furthermore, distinct other random parameters give enough choice to manipulate physical states governed by this model are observed. [ABSTRACT FROM AUTHOR]

This paper studies various forms of analytical solutions for mixed derivative nonlinear Schrödinger equation (MD-NLSE) which is used extensively in optical fiber. Our aim is to obtain lump solution (which is analytic in all directions), lump with one kink, rogue waves, periodic waves and multi-wave solutions for our governing model. We also discuss the interaction between periodic and lump, breather wave (which is a localized periodic wave solution of either discrete lattice or continuous media mathematical models), generalized breather, Ma-breather, Kuznetsov-Ma-breather and their corresponding rogue waves. At the end, we also present the dynamical behaviour of our solutions in terms of graphs in various dimensions. [ABSTRACT FROM AUTHOR]

Various forms of rational solitons, breathers, rogue wave, periodic wave and multiwave for Davydov solitons in α -helix proteins are described in this paper. We will figure out periodic wave, rogue wave, multiwave, M -shaped solutions, homoclinic breathers, kink cross rational solutions, periodic cross kink, periodic cross rational solitons, generalized breather, Akhmediev breather and Kuznetsov–Ma breather. We will also discuss some interactions between them. At the end, we will provide the graphical representation of our newly discovered solutions. [ABSTRACT FROM AUTHOR]

In this paper, we will study two various nonlinear models: the Atangana–Baleanu fractional system of equations for the ion sound and Langmuir waves (ISALWs) and Hirota Ramani equation to obtain variety of solitary wave solutions. We will obtain bright, dark, periodic wave and solitory wave for ISALWs equation. We will also retreived bell type, kink type, singular, Jacbion elliptic function, Weierstrass-elliptic function, hyperbolic functions, periodic functions and other solitary wave solutions for Hirota Ramani equation using Sub ODE technique under some constraint conditions. At the end we will present our solutions with the help of graphs in distinct dimensions. [ABSTRACT FROM AUTHOR]

In this article, we address dissipative nonlinear Schrödinger equation (d-NLSE) in (1 + 1) -dimensions influenced by spatial dissipations effects via applying logarithmic transformation and symbolic computation with the ansatz function method. The d-NLSE is applied to model the dissipative self-modulating monochromatic waves with dispersion. We analytically create the bright and dark optical soliton for d-NLSE. In addition, singular solutions of type-I, type-II, periodic, multiwave, M-shaped rational and their interactions with one and two kink waves, homoclinic breathers are derived. Furthermore, a few 3D, 2D and contour shapes will be shown to predict the wave dynamics. [ABSTRACT FROM AUTHOR]

This article recovers multiwave, homoclinic breather, M-shaped rational solitons and interaction of M-shaped rational solitons with single and double kinks for pure cubic nonlinear Schrödinger equation, with full nonlinearity, in a non-Kerr law media via the logarithmic transformation and symbolic computation with ansatz functions scheme. We use quadratic-cubic law and some suitable transformations involving trigonometric, exponential and hyperbolic functions to obtained various forms of stated solutions. In addition, we compute kink cross-rational solutions, periodic cross-rational solutions and periodic cross kink rational solutions for governing model. The proposed model is assumed with a few Hamiltonian perturbation terms that will sustain the balance between dispersion and self-trapping effect stemming from the nonlinear refractive index. Furthermore, the solitons behaviors for attained via different values parameters in the produced solutions are analyzed. [ABSTRACT FROM AUTHOR]

In this research, we study the chirped optical solitons (COS) for a nonlinear model with competing weakly nonlocal and parabolic law nonlinearities (CWN-PLNL). The Jacobi's elliptic function will be used to find the bright, dark, and solitary waves solution with some constraint conditions. The findings of this study might be beneficial in understanding how COS propagate in a weakly nonlocal parabolic law medium. We show our results in form of 3-D, 2-D, contour and density graphs. [ABSTRACT FROM AUTHOR]

In this paper, we will study the propagation properties of nonlinear periodic waves (PW) in a fiber optics for the coupled nonlinear Schrödinger equation with parabolic law with weak non-local nonlinearity (CNLSE-PLWNLNL). We will find the chirped periodic waves (CPW) by using some Jacobi elliptic functions (JEF) and also obtain some solitary waves (SW) like dark, bright, hyperbolic, singular, periodic and other solitons. The resultant chirp associated with each of these optical solitons (OS) will be observed dependent on pulse intensity. The graphical representation of these waves will also be presented. [ABSTRACT FROM AUTHOR]

Present study deals with the nonlinear Biswas–Milovic coupled system with Kudryashovs law of refractive index of magneto-optics waveguides. An extended modified auxiliary equation mapping scheme will be used in order to obtain some new solitary wave solutions like bright type, dark, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. Integrability of our governing model will also be investigated by Painleve test (P-test). Graphical results (2D, 3D and density plots) are also presented to display a comprehensive behavior of our outcomes. [ABSTRACT FROM AUTHOR]

This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation may be converted into plane systems. We use Hirota bilinear method to obtained these solutions. At the end, we present graphical representation of our results in various dimensions. [ABSTRACT FROM AUTHOR]

This study focuses on the Ablowitz–Kaup–Newell–Segur (AKNS) water waves equation. Painleve test (P-test) will be implemented to check the integrability of AKNS equation and an extended modified auxiliary equation mapping (EMAEM) architectonic is implemented to get a new set of traveling wave solutions like periodic and doubly periodic, bell type, kink, singular kink, anti-kink, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions. Furthermore, it is analyzed that the implemented algorithm is efficient and accurate for solving nonlinear evolution equations (NLEEs). Finally, graphical simulations (2D, 3D and contours) are also provided to illustrate the detailed behavior of the solution and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The current article is to address homoclinic breather solution, multi-waves, periodic -cross kink, the M-shaped rational solution and interaction solution of M-shaped rational soliton with Lump-two stripe and periodic waves for the perturbed nonlinear Schrödinger equation with quadratic cubic law nonlinearity by using the some ansatz transformations and symbolic computations. At the end, we discuss the graphical representation of our newly obtained results. [ABSTRACT FROM AUTHOR]

Lump (rational) waves and their interactions with kink and periodic waves, periodic cross-lump solutions will be discussed for (2+1)-dimensional Maccari-system in this paper. With the combination of rational, exponential, and trigonometric functions, we will study various lump soliton solutions. We will find out analytical solutions with interaction phenomenon and also describe them in graphical ways. [ABSTRACT FROM AUTHOR]

In this work, we use symbolic computation and ansatz function schemes, to investigate the soliton solutions for the nonlinear Schrödinger equation (NLSE) along with Kudryashov's quintuple self-phase modulation system (KQSPMS) including dual-form of nonlocal nonlinearity (DFNLN). We initially determine the ordinary differential (OD) form for this model through a variable transformation. Then we introduce numerous new dynamical soliton types: the M-shaped rational soliton, the M-shaped interaction between one and two stripe solitons, the periodic cross-M-shaped rational (PCMR) soliton, the periodic cross-kink (PCK) soliton, multi-waves, and the homoclinic breather soliton. Secondly, we determine the partial differential (PD) form for this model through a variable transformation. Moreover, a lump soliton, a periodic wave, a rogue wave, a lump interaction with a periodic and kink wave, and three different types of breather soliton will obtain. We'll demonstrate these solutions' unique structure and extremely interesting interaction behavior. We'll also use graphs (3-D and contour plots) to discuss the dynamics of the results after setting the parameters to the proper values. [ABSTRACT FROM AUTHOR]

In this research, we study a variety of solutions like periodic, exponential, rational, hyperbolic and Jacobian elliptic function solutions of Rangwala–Rao equation (RRE) by employing complete discrimination system for polynomial (CDSP) technique. We deduce the relevant travelling wave system from the original equation using the travelling wave transformation and generate a conserved quantity, the Hamiltonian, from it. With the aid of qualitative theory of differential equation and bifurcation theory of planar dynamical systems a variety of phase portraits to the relevant travelling wave system of RRE are explored. The CDSP approach is not only useful for generating soliton solutions but also for carrying out qualitative analysis. Furthermore, 3D and 2D graphs are displayed for some of the soliton solutions of RRE. [ABSTRACT FROM AUTHOR]

In this paper, using the Hirota bilinear method, we investigate the perturbed Gerdjikov–Ivanov equation (PGIE) for lump soliton, rogue wave, periodic and kink cross rational solutions, homoclinic breathers, M-shaped and many other interactions. All these solutions have so many real life applications for example lump wave help to study the behavior of vortices and eddies in the ocean, which are used for climate modeling and fisheries management. Rogue waves are used in maritime safety, M-shaped solitons are used in optical fiber communications to transmit data over long distances without distortion, improving the efficiency and reliability of high-speed data transmission. Breathers can be used in fiber optic systems to generate ultrafast optical pulses, which have applications in telecommunications and laser technology. We also discuss the dynamical behaviour of our solutions in various dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we will compute the conservation laws (CLs) of Chen–Lee–Liu equation (CLLE) with the help of scaling invariance technique. We will use Euler and Homotopy operators for the evaluation of conserved densities and fluxes. We will also obtain optical dromions with the help of Unified method (UM). By using this method, we will get domain walls, solitary wave and elliptic wave solutions. Moreover, we will investigate the stability as well as the integrability of the governing model by using linear stability technique and Painlevé analysis respectively. [ABSTRACT FROM AUTHOR]

In this paper, we investigated a new form of nonlinear Schrödinger equation (NLSE), namely the Biswas–Arshed model (BAM) for the analysis of complete integrability with the help of Painlevé test (P -test). By applying this test, we analyze the singularity structure of the solutions of BAM, knowing the fact that the absence of specific sort of singularities like moveable branch points is a patent signal for the complete integrability of the discussed model. Passing the P -test is a powerful indicator that the studied model is resolvable by means of inverse scattering transformation (IST). [ABSTRACT FROM AUTHOR]

We investigate the rational solitons of the Kraenkel–Manna–Merle (KMM) system in ferrites via symbolic computation with the ansatz functions technique and logarithmic transformation. The KMM system describes the propagations of the ferromagnetic particles in ferrite materials. Multiwave solitons are reported by using the three-wave technique. Homocentric breathers (HBs) approach is also applied to build new forms of exact solutions. We construct M-shaped solitons and their dynamics are shown via the appropriate values of parameters. Two types of interactions for rational soliton with kink wave are investigated. Additionally, kink cross-rational solitons (KCRSs) and periodic cross-rational solitons (PCRSs) are examined via suitable transformation. [ABSTRACT FROM AUTHOR]