Jacobi Elliptic Function Method for (2+1)-Dimensional Maccari System with Multiplicative Brownian Noise: Solitary Wave Solutions, Nonlinear Dynamics and Numerical Verification

Dynamical analysis, chaotic behavior and soliton solutions of the generalized unstable space–time fractional nonlinear Schrödinger equation

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

A reliable algorithm based on Haar wavelet and Runge-Kutta method for the numerical solutions of (1+1)- and (1+2)-dimensional nonlinear parabolic partial differential equations

This study addresses the approximate solution of (1+1)- and (1+2)-dimensional nonlinear parabolic partial differential equations with initial and Dirichlet boundary conditions. The proposed hybrid scheme integrates the Haar wavelet with the fourth-order Runge-Kutta (RK-4) method. Spatial discretization via Haar wavelet...

Dynamical analysis and closed-form soliton solutions for the doubly dispersive equation

The purpose of this work is to examine new exact soliton solutions for the doubly dispersive equation (DDE) by utilizing a finite series in terms of Jacobi elliptic functions (JEFs). For the exact analytical solution of nonlinear partial differential equations (NLPDEs), the JEF expansion approach is frequently employ...

New classes of wave solutions for nonlinear conformable space-time PDEs via the Riccati sub-equation approach: analysis of the Bateman-Burgers, Clannish Random Walker's parabolic, and Estevez-Mansfield-Clarkson equations

In this article, we study and introduce travelling wave properties of some nonlinear space-time fractional partial differential equations in applied physics, and the most important is to find analytical solutions for them. We treated in this study the nonlinear space-time fractional Bateman-Burgers equation, the Clanni...

Investigating Chaos and Exact Solutions in Electromagnetic Wave Dynamics Governed by the Time-Fractional Drinfel’d–Sokolov–Wilson Equation

Nonlinear electromagnetic wave propagation in complex plasma environments has attracted considerable attention due to its important applications in nonlinear optics, plasma physics, space science, and communication technologies. In the present study, a time-fractional Drinfel’d–Sokolov–Wilson equation (DSWE) is investi...