A Theoretical Model for Nonlinear Plasma Waves using a Modified KdV-Burgers Framework

This paper develops a theoretical model to describe nonlinear wave dynamics in a magnetized plasma. Starting from a reduced set of fluid equations, we employ a reductive perturbation technique to derive a Korteweg-de Vries-Burgers (KdV-Burgers) equation. The derivation yields explicit, detailed expressions for the three fundamental coefficients governing the evolution: the nonlinear coefficient P, the dispersive coefficient Q, and the dissipative coefficient R. This unnormalized evolution equation provides a direct and physically transparent framework for analyzing the formation and propagation of nonlinear structures like solitons and shock waves in various plasma environments. Furthermore, we present a comprehensive nonlinear dynamics and stability analysis, including phase portraits, potential landscapes, and Lyapunov exponents, to characterize the system's behavior across different dynamical regimes.