A Data-Driven Extended KdV--Burgers Framework for Nonlinear Plasma Wave Analysis

Abstract

We present a novel framework that integrates NASA’s magnetospheric multiscale (MMS) mission data with advanced theoretical modeling to study nonlinear plasma wave dynamics in space environments. By developing an extended reductive perturbation technique (E-RPT), we derive a modified Korteweg–de Vries (KdV)–Burgers equation with forcing terms that captures higher order nonlinear, dispersive, and dissipative effects in magnetospheric plasmas. Three physically distinct configurations are examined: a complete model, an isothermal plasma approximation, and a practical approximation using second-order quantities. Empirical validation draws on MMS observations in which measured electric fields, magnetic fields, and plasma parameters are normalized and fed into our Solstorm-PY simulation framework. The analysis reproduces observed shock formations, with the system parameters sitting near critical bifurcation thresholds. Our investigation of the nonlinear dynamics encompasses phase-space analysis, stability characterization through eigenvalue distributions, bifurcation analysis across parameter spaces, and computation of Lyapunov exponents. The three configurations display markedly different dynamical regimes, ranging from weakly chaotic to strongly stable behavior. Identifying the critical stability transitions defines viable operating regimes for plasma control systems, laboratory experiments, and turbulence studies. This work establishes a paradigm for data-validated theoretical development in space plasma physics, bridging in situ spacecraft measurements and nonlinear dynamical systems analysis, with direct implications for space weather prediction and plasma control.