TY - JOUR
T1 - Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation
AU - Hu, Wei Peng
AU - Deng, Zi Chen
AU - Qin, Yu Yue
AU - Zhang, Wen Rong
PY - 2012/6
Y1 - 2012/6
N2 - In the present paper, a general solution involving three arbitrary functions for the generalized (2+1)- dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equation, is first introduced by means of the Wiess, Tabor, Carnevale (WTC) truncation method. And then multisymplectic formulations with several conservation laws taken into account are presented for the generalized (2+1)- dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from the general solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent to the Preissmann scheme. From the results of the numerical experiments, we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized (2+1)- dimensional KdV-mKdV equation while preserve approximately the conservation laws.
AB - In the present paper, a general solution involving three arbitrary functions for the generalized (2+1)- dimensional KdV-mKdV equation, which is derived from the generalized (1+1)-dimensional KdV-mKdV equation, is first introduced by means of the Wiess, Tabor, Carnevale (WTC) truncation method. And then multisymplectic formulations with several conservation laws taken into account are presented for the generalized (2+1)- dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from the general solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent to the Preissmann scheme. From the results of the numerical experiments, we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized (2+1)- dimensional KdV-mKdV equation while preserve approximately the conservation laws.
KW - Conservation law
KW - Generalized (2+1)-dimensional KdV-mKdV equation
KW - Jacobi elliptic function
KW - Multi-symplectic
KW - Periodic wave solution
UR - http://www.scopus.com/inward/record.url?scp=84865475722&partnerID=8YFLogxK
U2 - 10.1007/s10409-012-0070-2
DO - 10.1007/s10409-012-0070-2
M3 - 文章
AN - SCOPUS:84865475722
SN - 0567-7718
VL - 28
SP - 793
EP - 800
JO - Acta Mechanica Sinica/Lixue Xuebao
JF - Acta Mechanica Sinica/Lixue Xuebao
IS - 3
ER -