Multi-symplectic method for peakon-antipeakon collision of quasi-Degasperis-Procesi equation

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• 作者：Weipeng Hu^a ; ^b ; ^c ; ^{wphu@nwpu.edu.cn" class="auth_mail} ; Zichen Deng^a ; ^b ; Yu Zhang^a
• 关键词：Multi-symplectic method ; Quasi-Degasperis&ndash ; Procesi equation ; B-family equation ; Jump discontinuity ; Peakon&ndash ; antipeakon collision
• 刊名：Computer Physics Communications
• 出版年：July 2014
• 年：2014
• 卷：185
• 期：7
• 页码：2020-2028
• 全文大小：873 K

文摘

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$b=3$ and b=4$b=4$). 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.