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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.

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.

This paper retrieves the investigation of rational solitons via symbolic computation with logarithmic transformation and ansatz functions approach for the [Formula: see text]-dimensional generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt (GKDKK) equation in fluid mechanics, ocean dynamics and plasma physics. We find two categories of M-shaped rational solitons and their dynamics will be revealed through graphs by choosing the suitable values of involved parameters. In addition, two categories of M-shaped rational solitons and their interactions with kink waves will be analyzed. Furthermore, homoclinic breathers, multi-wave and kink cross rational solitons will be investigated. The periodic, rational, dark, bright, Weierstrass elliptic function and positive soliton solutions will also be retrieved with the aid of Sub-ODE approach. Moreover, stability characteristics of solutions will be evaluated.

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.

This paper discusses the generalized [Formula: see text]-dimensional Hietarinta-type fourth-order nonlinear equation (GHTE) and Resonant nonlinear Schrödinger equation (RNLSE). We will study the soliton solutions of the GHTE as well as RNLSE by the renowned, efficient and successful method called sub-ODE technique. The solutions are categorized as dark soliton, periodic, rational, positive, hyperbolic and Weierstrass elliptic solutions (WES). Stability analysis of the solutions is performed for both the models. Later on, these results will be displayed graphically by 3D, 2D, contour, density and streamline plots which describe the behavior of the waves.

This paper deals with the evaluation of multiwave, homoclinic breather, [Formula: see text]-shaped rational solitons and interaction of [Formula: see text]-shaped rational solitons with single and double kinks for [Formula: see text]-dimensional longitudinal wave equation via the logarithmic transformation and symbolic computation with ansatz functions method. We will obtain two types of [Formula: see text]-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 [Formula: see text]-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.

This paper studies the Lax pair (LP) of the [Formula: see text]-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.

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), [Formula: see text]-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 [Formula: see text]-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.

In this study, we give the numerical scheme to the stochastic nonlinear advection diffusion equation. This models is considered with white noise (or random process) having same intensity by changing frequencies. Furthermore, the stability and consistency of proposed scheme are also discussed. Moreover, it is concerned about the analytical solutions, the Riccati equation mapping method is adopted. The different families of single (shock and singular) and mixed (complex solitary-shock, shock-singular, and double-singular) form solutions are obtained with the different choices of free parameters. The graphical behavior of solutions is also depicted in 3D and corresponding contours.

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.

This paper studies the soliton solutions for Embedded soliton (ES) generating model with [Formula: see text] 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.

The principle goal of the paper is to present proficient limited contrast finite difference schemes to execute on the nonlinear coupled partial differential system which emulate the overseeing differential framework. In this paper, more consideration is given to the exactness and security of the proposed numerical schemes by review consistency and union of the arrangement which can be seen from figures and information tables. For the nonlinear differential system, mesh independent results are expensive which are accommodated by the generation of block tridiagonal matrix structures (inherent properties of schemes) which are measured in terms of [Formula: see text] & [Formula: see text] norms which lead to a superb concurrence with the investigative arrangement.

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 [Formula: see text], [Formula: see text], 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.

In this paper, we address a newly nonlinear Schrödinger equation (NLSE) in [Formula: see text]-dimensions influenced by cubic–quintic–septic law nonlinearity and spatial dissipations effects. We properly construct the dark and bright optical soliton solutions for our governing model. Furthermore, periodic, other singular solutions, multiwave, homoclinic breather, [Formula: see text]-shaped rational and their interaction with kink waves of various structures will be derived. In addition to this, some 3D, 2D and contour profiles will be added to anticipate the wave dynamics.

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.

Various forms of rational solitons, breathers, rogue wave, periodic wave and multiwave for Davydov solitons in [Formula: see text]-helix proteins are described in this paper. We will figure out periodic wave, rogue wave, multiwave, [Formula: see text]-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.

In this paper, we study the perturbed nonlinear Schrödinger equation (P-NLSE) representing the propagation of waves and may be regarded as a nonlinear complicated physical model. We use the modified extended Tan hyperbolic function (METhF) approach and the [Formula: see text]-expansion approach to construct some new traveling wave structures. Several solutions have been found including dark soliton, periodic-type solitons, bell-shaped solitons, single bell-shaped solitons. We also show a graphical representation of a number of exact solutions to the dynamical model together with a description of their behavior. The proposed techniques can also be extended to various nonlinear evolution models in mathematical physics and engineering.

The shallow water wave model is one of the completely integrable models illustrating many physical problems. In this article, we investigate new exact wave structures to Kadomtsev–Petviashvili–Benjamin–Bona–Mahony and the Benney–Luke equations which explain the behavior of waves in shallow water. The exact structures are expressed in the shapes of hyperbolic, singular periodic, rational as well as solitary, singular, shock, shock-singular solutions. An efficient computational strategy namely modified direct algebraic method is employed to construct the different shapes of wave structures. Moreover, by fixing parameters, the graphical representations of some solutions are plotted in terms of three-dimensional, two-dimensional and contour plots, which explain the physical movement of the attained results. The accomplished results show that the applied computational technique is valid, proficient, concise and can be applied in more complicated phenomena.

This paper retrieves different types of solutions such as [Formula: see text]-shaped rational solutions with one and two kinks, homoclinic breather, multi-waves, periodic cross-kink and kink-cross rational solutions for Radhakrishnan–Kundu–Lakshmanan equation (RKLE). We will study the [Formula: see text]-shaped interaction with rogue and kink, we will also obtain the [Formula: see text]-shaped interaction with periodic and kink, periodic cross-rational solutions. At the end, we will express the graphical representation for our newly achieved solutions.