Numerical simulation for solitary wave of Klein-Gordon-Zakharov equation based on the lattice Boltzmann model

Abstract This work reports a study of Klein–Gordon–Zakharov equation by using the lattice Boltzmann method. The Klein–Gordon–Zakharov equation describes the interaction of the Langmuir wave and the ion acoustic wave in plasma. Numerical simulations of the constructed lattice Boltzmann model for the Klein–Gordon–Zakharov equation show the propagation and the interaction of the (1+1) and (2+1) dimensional solitary waves. These simulation results are examined and compared by using different parameters and different schemes. This work indicates that the lattice Boltzmann method can be a very effective tool for the simulation of Klein–Gordon–Zakharov equation.

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