1.
Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle.
Sci Rep
; 9(1): 15883, 2019 Nov 04.
Artigo
em Inglês
| MEDLINE
| ID: mdl-31685898
RESUMO
The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well.