Effects of additive noise and variable coefficients on the exact solutions of the stochastic Kawahara equation

This paper investigates exact solutions and soliton dynamics in a stochastic Kawahara equation with variable coefficients and additive noise. Using Galilean transformation, the original system is transformed to a variable coefficient equation coupled with a solvable stochastic ODEs. Exact solutions are derived via Painleve truncation expansion and validated through an improved Zabusky-Kruskal finite difference scheme. Quantitative analysis reveals that variable coefficients induce waveform deformation through amplitude-phase modulation, while governs soliton stability via amplitude-width interactions. Crucially, increasing wave numbers suppress diffusion by amplifying amplitude without altering width, thereby slowing dissipation. The methodology uniquely couples deterministic integrability with stochastic dynamics, differing from conventional approaches. demonstrate synergistic effects of nonlinear dispersion, variable coefficients, and noise on soliton evolution, providing new insights for stochastic fifth-order dispersive systems.