TY - JOUR
T1 - Multisymplectic method for the Camassa-Holm equation
AU - Zhang, Yu
AU - Deng, Zi Chen
AU - Hu, Wei Peng
N1 - Publisher Copyright:
© 2016, Zhang et al.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - Camassa-Holm equation
KW - conservation law
KW - multisymplectic method
KW - peaked wave solution
UR - http://www.scopus.com/inward/record.url?scp=84953730233&partnerID=8YFLogxK
U2 - 10.1186/s13662-015-0724-z
DO - 10.1186/s13662-015-0724-z
M3 - 文章
AN - SCOPUS:84953730233
SN - 1687-1839
VL - 2016
SP - 1
EP - 12
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 7
ER -