Soliton solution and bifurcation analysis of the KP–Benjamin–Bona–Mahoney equation with power law nonlinearity

Abstract

This paper studies the Kadomtsev-Petviashvili-Benjamin-Bona-Mahoney equation with power law nonlinearity. The traveling wave solution reveals a non-topological soliton solution with a couple of constraint conditions. Subsequently, the dynamical system approach and the bifurcation analysis also reveals other types of solutions with their corresponding restrictions in place.

Nonlinear dynamics of a generalized higher-order nonlinear Schrödinger equation with a periodic external perturbation

“…In this part, we investigate the bifurcation and chaotic motions of Eq. (2) which are the interesting nonlinear phenomena and have great applications in many fields such as the technological, engineering, telecommunications, ecology [27,28]. The addition of a perturbation can lead to the system non-integrable.…”

“…When Γ = 0, Eq. (1) can be used to describe the slowly varying electromagnetic waves in optical fibers [14,27,28]. However, for the ultrashort pulses propagation in the high-bit-rate and long-distance communication, some higher-order linear and nonlinear terms have to be incorporated into the NLS equation [14].…”

Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients

“…Some of them are soliton solutions, solitary wave solutions, cnoidal and snoidal waves, periodic solutions, topological soliton solutions as well as various other types, for more references see also . In the nonlinear science, many important phenomena in various fields can be described by NLEEs [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Recently, much attention has been paid to the variable-coefficient nonlinear equations which can describe many nonlinear phenomena more realistically than their constant-coefficient ones.…”