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Numerical study of the nonlinear combined sine-cosine-Gordon equation with the lattice Boltzmann method. (English) Zbl 1259.65130
Summary: A lattice Boltzmann model is developed for solving the combined sine-cosine-Gordon equation through selecting equilibrium distribution functions properly. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. Some problems, which have exact solutions, are validated by the present model. From the simulations, we find that the numerical results agree well with the exact solutions or better than the numerical solutions reported in previous studies. The study indicates that the present method is very effective and accurate. The present model can be used to solve more other nonlinear wave problems.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
35Q40 PDEs in connection with quantum mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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