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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 discusses the generalized (2 + 1) -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. [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 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]

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 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]

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 L 2 & L ∞ norms which lead to a superb concurrence with the investigative arrangement. [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]

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]

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 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 ( G ′ G 2 ) -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. [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 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]