TY - JOUR
T1 - Multi-symplectic method for peakon-antipeakon collision of quasi-Degasperis-Procesi equation
AU - Hu, Weipeng
AU - Deng, Zichen
AU - Zhang, Yu
PY - 2014/7
Y1 - 2014/7
N2 - Focusing on the local geometric properties of the shockpeakon for the Degasperis-Procesi equation, a multi-symplectic method for the quasi-Degasperis-Procesi equation is proposed to reveal the jump discontinuity of the shockpeakon for the Degasperis-Procesi equation numerically in this paper. The main contribution of this paper lies in the following: (1) the uniform multi-symplectic structure of the b-family equation is constructed; (2) the stable jump discontinuity of the shockpeakon for the Degasperis-Procesi equation is reproduced by simulating the peakon-antipeakon collision process of the quasi-Degasperis-Procesi equation. First, the multi-symplectic structure and several local conservation laws are presented for the b-family equation with two exceptions (b=3 and b=4). And then, the Preissman Box multi-symplectic scheme for the multi-symplectic structure is constructed and the mathematical proofs for the discrete local conservation laws of the multi-symplectic structure are given. Finally, the numerical experiments on the peakon-antipeakon collision of the quasi-Degasperis-Procesi equation are reported to investigate the jump discontinuity of shockpeakon of the Degasperis-Procesi equation. From the numerical results, it can be concluded that the peakon-antipeakon collision of the quasi-Degasperis-Procesi equation can be simulated well by the multi-symplectic method and the simulation results can reveal the jump discontinuity of shockpeakon of the Degasperis-Procesi equation approximately.
AB - Focusing on the local geometric properties of the shockpeakon for the Degasperis-Procesi equation, a multi-symplectic method for the quasi-Degasperis-Procesi equation is proposed to reveal the jump discontinuity of the shockpeakon for the Degasperis-Procesi equation numerically in this paper. The main contribution of this paper lies in the following: (1) the uniform multi-symplectic structure of the b-family equation is constructed; (2) the stable jump discontinuity of the shockpeakon for the Degasperis-Procesi equation is reproduced by simulating the peakon-antipeakon collision process of the quasi-Degasperis-Procesi equation. First, the multi-symplectic structure and several local conservation laws are presented for the b-family equation with two exceptions (b=3 and b=4). And then, the Preissman Box multi-symplectic scheme for the multi-symplectic structure is constructed and the mathematical proofs for the discrete local conservation laws of the multi-symplectic structure are given. Finally, the numerical experiments on the peakon-antipeakon collision of the quasi-Degasperis-Procesi equation are reported to investigate the jump discontinuity of shockpeakon of the Degasperis-Procesi equation. From the numerical results, it can be concluded that the peakon-antipeakon collision of the quasi-Degasperis-Procesi equation can be simulated well by the multi-symplectic method and the simulation results can reveal the jump discontinuity of shockpeakon of the Degasperis-Procesi equation approximately.
KW - B-family equation
KW - Jump discontinuity
KW - Multi-symplectic method
KW - Peakon-antipeakon collision
KW - Quasi-Degasperis-Procesi equation
UR - http://www.scopus.com/inward/record.url?scp=84901627178&partnerID=8YFLogxK
U2 - 10.1016/j.cpc.2014.04.006
DO - 10.1016/j.cpc.2014.04.006
M3 - 文章
AN - SCOPUS:84901627178
SN - 0010-4655
VL - 185
SP - 2020
EP - 2028
JO - Computer Physics Communications
JF - Computer Physics Communications
IS - 7
ER -