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Multi-symplectic methods for the Itô-type coupled KdV equation. (English) Zbl 1244.65232
Summary: We find that the Itô-type coupled Korteweg-de Vries (KdV) equation can be written as a multi-symplectic Hamiltonian partial differential equation. Then, multi-symplectic Fourier pseudospectral method and multi-symlpectic wavelet collocation method are constructed for this equation. In the numerical experiments, we show the effectiveness of the proposed methods. Some comparisons between the proposed methods are also made with respect to global conservation properties.
MSC:
65P10Numerical methods for Hamiltonian systems including symplectic integrators
37M15Symplectic integrators (dynamical systems)
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q53KdV-like (Korteweg-de Vries) equations
65M70Spectral, collocation and related methods (IVP of PDE)
65T60Wavelets (numerical methods)