Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation

Abstract In this paper, we develop a novel multi-symplectic wavelet collocation method for solving multi-symplectic Hamiltonian system with periodic boundary conditions. Based on the autocorrelation function of Daubechies scaling functions, collocation method is conducted for the spatial discretization. The obtained semi-discrete system is proved to have semi-discrete multi-symplectic conservation laws and semi-discrete energy conservation laws. Then, appropriate symplectic scheme is applied for time integration, which leads to full-discrete multi-symplectic conservation laws. Numerical experiments for the nonlinear Schrodinger equation and Camassa–Holm equation show the high accuracy, effectiveness and good conservation properties of the proposed method.

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