This paper examines the propagation of M-shape solitons and their interactions with kink waves to the (2 + 1)-dimensional integrable Schwarz-Korteweg-de Vries (ISKdV) problem by applying the symbolic computation with ansatz functions technique and logarithmic transformation. The governing model usually appears in the nonlinear shallow water waves and fluid mechanics. We discuss various nonlinear waves like multiwave solutions (MSs), homoclinic breather (HB), M-shape solitons, single exponential form (one-kink), and double exponential form (two-kink). These waves have lot of applications in fluid dynamics, nonlinear optics, chemical reaction networks, biological systems, climate science, and material science. We also study interaction among M-shape solitons with kink wave. At the end, we discuss the stability characteristics of all solutions.

In an optical fibre, we investigate the propagation properties of nonlinear periodic waves (PW) for a generalized mixed nonlinear Schrödinger (GMNLS) equation. The Jacobi elliptic (JE) solutions will be used to find the nonlinear chirp. The chirp varies with two intensity-dependent chirping terms are included in the linear section of the pulse chirp. The presence of the newly discovered periodic waves will be discussed in terms of fibre parameter conditions. The long-wave limit generates a wide range of solitary pulse forms, including topological, non topological, dark, kink, hyperbolic and periodic solitary waves (SW). Our findings show that for periodic and solitary waves, a nonlinear chirp obtains. Finally, under finite perturbations, the stability of these nonlinearly chirped solutions will be quantitatively investigated.

This paper's main focus is on chirped pulses (CP) for a cubic-quintic nonlinear non-paraxial pulse propagation (CQ-NNP-PP) model. Chirped solitons are a relatively new single wave phenomena. The exact CPs generate from the derivative nonlinear Schrödinger equations (NLSE). Chirp is a signal with a changing frequency over time. CPs are used in spread spectrum communications as well as some sonar and radar devices. The propagation of CPs in fibre optics is getting popular due to a wide range of applications in amplification and pulse compression. In an NLSE, the dispersion management (DM) term can influence the velocity of chirp-free nonautonomous soliton but has no effect on its shape. When there is no gain, the classical optical soliton can be expressed with a variable dispersion term and nonlinearity. DM can impact the shape and motion of non autonomous solitons for CPs. We obtain hyperbolic and periodic solutions, as well as a class of solitary wave (SW) solutions such as bright, dark, singular and bell soliton solutions. The governing model will be analyzed with the aid of Jacobian elliptic functions (JEF). We also show accomplished results in 3D and 2D structures.

The Lugiato–Lefever equation is a cubic nonlinear Schrödinger equation (NLSEs) that occurs as a model in nonlinear optics and includes damping, detuning, and driving. On the basis of a model of coupled nonlinear NLSEs, the trapping behaviour of two chirped solitons creating a bound state in a single-mode birefringent fibre is explored. The positive initial chirp is critical for managing the soliton trapping threshold amplitude without creating excessive pulse broadening. In this paper, the Jacobi elliptic function (JE) technique, which is one of the efficient integration procedures, is used to investigate chirped elliptic and solitary wave solitons (SWS) to NLSEs with generalized Longitudinal Lugiato Lefever (GLLL) equation. As a result, the bright, single, dark, bell, kink soliton, and other solutions of the governing model are found. In further, we demonstrate successful results in 3D, 2D and contour structures.