Finite Element Method for Stochastic Extended KdV Equations

TL;DR

This paper applies the finite element method to solve stochastic extended KdV equations, analyzing the stability of solitons and cnoidal waves under stochastic forces in shallow water models.

Contribution

It introduces a numerical approach using finite element methods for stochastic extended KdV equations and examines wave robustness under stochastic influences.

Findings

Main waves remain stable despite stochastic forces

Cnoidal and solitary waves show robustness against distortions

Second order dynamics effects are often obscured by stochastic forces

Abstract

The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves under stochastic forces are presented. Though small effects originating from second order dynamics may be obscured by stochastic forces, the main waves, both cnoidal and solitary ones, remain very robust against any distortions.