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Zbl 1244.65232
Chen, Yaming; Song, Songhe; Zhu, Huajun
Multi-symplectic methods for the Itô-type coupled KdV equation. (English)
[J] Appl. Math. Comput. 218, No. 9, 5552-5561 (2012). ISSN 0096-3003

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 2000:: *65P10 Hamiltonian systems including symplectic integrators
37M15 Symplectic integrators
37K10 Completely integrable systems etc.
35Q53 KdV-like equations
65M70 Spectral, collocation and related methods (IVP of PDE)
65T60 Wavelets

Keywords: Itô-type coupled KdV equation; multi-symplectic Fourier pseudospectral method; wavelet collocation method; Korteweg-de Vries equation; multi-symplectic Hamiltonian equation; numerical experiments

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Zentralblatt MATH Berlin [Germany]