摘要We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation. Two test problems, the motion of a single solitary wave and interaction of solitary waves, are simulated. Numerical experiments show that the present scheme not only provides highly accurate numerical solutions, but also displays good performance in preserving the three integral invariants during long-time computation. Especially, the excellent ability to preserve the higher order invariant indicates that the proposed algorithm is robust and reliable.
Abstract：We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation. Two test problems, the motion of a single solitary wave and interaction of solitary waves, are simulated. Numerical experiments show that the present scheme not only provides highly accurate numerical solutions, but also displays good performance in preserving the three integral invariants during long-time computation. Especially, the excellent ability to preserve the higher order invariant indicates that the proposed algorithm is robust and reliable.
CAI Jia-Xiang, MIAO Jun. New Explicit Multisymplectic Scheme for the Complex Modified Korteweg-de Vries Equation[J]. 中国物理快报, 2012, 29(3): 30201-030201.
CAI Jia-Xiang, MIAO Jun. New Explicit Multisymplectic Scheme for the Complex Modified Korteweg-de Vries Equation. Chin. Phys. Lett., 2012, 29(3): 30201-030201.
[1] Muslu G M and Erabay H A 2003 Comput. Math. Appl. 45 503 [2] Taha T R 1994 Math. Comput. Simul. 37 461[3] Ismail M S 2008 Appl. Math. Comput. 202 520 [4] Ismail M S 2009 Commun. Nonlinear Sci. Numer. Simul. 14 749 [5] Uddina M et al 2009 Comput. Math. Appl. 58 566 [6] Korkmaz A and Da? I 2009 Comput. Phys. Commun. 180 1516 [7] Aydin A and Korasözen B 2010 J. Math. Phys. 51 083511 [8] Marsden J E et al 1999 Commun. Math. Phys. 199 351 [9] Bridges T J and Reich S 2001 Phys. Lett. A 284 184 [10] Ascher U M and McLachlan R I 2004 Appl. Numer. math. 48 255 [11] Wang Y S et al 2008 Chin. Phys. Lett. 25 1538[12] Cai J X et al 2009 J. Math. Phys. 50 033510 [13] Cai J X 2010 J. Comput. Appl. Math. 234 899 [14] Hong J L et al 2009 J. Comput. Phys. 228 3517 [15] Bridges T J and Reich S 2001 Physica D 152 491 [16] Chen J B and Qin M Z 2001 Electron. Trans. Numer. Anal. 12 193[17] Wang J 2009 J. Phys. A: Math. Theor. 42 085205 [18] Hong J L and Kong L H 2010 Commun. Comput. Phys. 7 613 [19] Kong L H et al 2010 Comput. Phys. Commun. 181 1369 [20] Lv Z Q et al 2011 Chin. Phys. Lett. 28 060205
2012, Vol. 29 
