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Multisymplectic method for the Camassa-Holm equation.
- Source :
- Advances in Difference Equations; 1/8/2016, Vol. 2016 Issue 1, p1-12, 12p
- Publication Year :
- 2016
-
Abstract
- The Camassa-Holm equation, a completely integrable evolution equation, contains rich geometric structures. For the existence of the bi-Hamiltonian structure and the so-called peaked wave solutions, considerable interest has been aroused in the last several decades. Focusing on local geometric properties of the peaked wave solutions for the Camassa-Holm equation, we propose the multisymplectic method to simulate the propagation of the peaked wave in this paper. Based on the multisymplectic theory, we present a multisymplectic formulation of the Camassa-Holm equation and the multisymplectic conservation law. Then, we apply the Euler box scheme to construct the structure-preserving scheme of the multisymplectic form. Numerical results show the merits of the multisymplectic scheme constructed, especially the local conservative properties on the wave form in the propagation process. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16871839
- Volume :
- 2016
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- 112154324
- Full Text :
- https://doi.org/10.1186/s13662-015-0724-z