Emergence of complex soliton structures and qualitative dynamics in the (2+1)-dimensional nonlinear Schrödinger equation

Demonstration of Soliton Wave Structures in a Higher-Dimensional Nonlinear Physical Model: Dynamic Insights into Sensitivity, Bifurcation, and Chaos

This article presents a comprehensive analytical and dynamical investigation of the (4+1)-dimensional variable-coefficient generalized Kadomtsev Petviashvili equation (vc-gKP). Exact analytical solutions are constructed using the modified Khater method, constructing a diverse class of localized and propagating wave str...

Dynamical Behavior and Nonlinear Wave Structures of a (3+1)‐Dimensional Generalized Ito Equation

This study describes a novel connection between the algebraic integrable structure and the geometric dynamical behavior of the ‐dimensional generalized Ito equation. By considering different types of real eigenvalues, we construct Wronskian determinant type analytic solutions that include rational, positon, negaton a...

Analytical investigation of a novel (3+1)-dimensional nonlinear schrödinger equation with stability analysis

Bifurcation analysis, conservation laws and dynamics of solitons solutions for the Kundu–Eckhaus equation and its applications

Soliton solutions and dynamical bifurcation analysis of the Yajima-Oikawa equations

The Yajima–Oikawa equations describes the resonant interaction between ion sound waves and Langmuir waves in plasma. Despite its importance, the detailed dynamical behavior of this model has not been comprehensively explored. In this work, we present a unified analytical and dynamical framework that combines exact so...

On the soliton dynamics, bifurcation analysis and perturbed induced chaotic behaviors of the time-fractional Boussinesq equation

Abstract The time-fractional Boussinesq equation helps in the modeling of various physical phenomena, such as shallow water waves and coastal engineering, to model tsunamis. This paper investigates the time-fractional Boussinesq equation, after introducing memory effect through the time fractional parameter β ∈ (0, 1]....