Numerical simulation for the motions of nonautonomous solitary waves of a variable-coefficient forced Burgers equation via the lattice Boltzmann method

TL;DR

This paper develops a lattice Boltzmann method to simulate nonautonomous solitary waves in a variable-coefficient forced Burgers equation, demonstrating its accuracy and efficiency through numerical examples.

Contribution

It introduces a tailored lattice Boltzmann approach for the variable-coefficient forced Burgers equation, validated by theoretical and numerical consistency.

Findings

LBM accurately reproduces theoretical soliton solutions

The method effectively captures dispersive and external-force effects

Numerical results align well with analytical predictions

Abstract

The lattice Boltzmann method (LBM) for the variable-coefficient forced Burgers equation (vc-FBE) is studied by choosing the equilibrium distribution and compensatory functions properly. In our model, the vc-FBE is correctly recovered via the Chapman-Enskog analysis. We numerically investigate the dynamic characteristics of solitons caused by the dispersive and external-force terms. Four numerical examples are given, which align well with the theoretical solutions. Our research proves that LBM is a satisfactory and efficient method for nonlinear evolution equations with variable coefficients.