A new explicit multisymplectic integrator for the Kawahara-type equation

doi:10.1088/1674-1056/23/3/030204

中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30204-030204.doi: 10.1088/1674-1056/23/3/030204

A new explicit multisymplectic integrator for the Kawahara-type equation

蔡文君, 王雨顺

Key Laboratory for NSLSCS of Jiangsu Province, School of Mathematics and Sciences, Nanjing Normal University, Nanjing 210023, China

收稿日期:2013-11-13 修回日期:2013-12-16 出版日期:2014-03-15 发布日期:2014-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11271195 and 11271196) and the Project of Graduate Education Innovation of Jiangsu Province, China (Grant No. CXZZ12-0385).

A new explicit multisymplectic integrator for the Kawahara-type equation

Cai Wen-Jun (蔡文君), Wang Yu-Shun (王雨顺)

Key Laboratory for NSLSCS of Jiangsu Province, School of Mathematics and Sciences, Nanjing Normal University, Nanjing 210023, China

Received:2013-11-13 Revised:2013-12-16 Online:2014-03-15 Published:2014-03-15
Contact: Wang Yu-Shun E-mail:wangyushun@njnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11271195 and 11271196) and the Project of Graduate Education Innovation of Jiangsu Province, China (Grant No. CXZZ12-0385).

摘要/Abstract

摘要： We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Numerical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations.

关键词: Kawahara-type equation, multisymplectic integrator, Euler-box scheme, adjoint scheme

Abstract: We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Numerical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations.

Key words: Kawahara-type equation, multisymplectic integrator, Euler-box scheme, adjoint scheme

中图分类号: (Finite-difference methods)

02.70.Bf

03.65.Ge (Solutions of wave equations: bound states) 45.10.Na (Geometrical and tensorial methods) 47.10.Df (Hamiltonian formulations)

蔡文君, 王雨顺. A new explicit multisymplectic integrator for the Kawahara-type equation[J]. 中国物理B, 2014, 23(3): 30204-030204.

Cai Wen-Jun (蔡文君), Wang Yu-Shun (王雨顺). A new explicit multisymplectic integrator for the Kawahara-type equation[J]. Chin. Phys. B, 2014, 23(3): 30204-030204.

参考文献 28

[1]	Kawahara T 1972 J. Phys. Soc. Jpn. 33 260
[2]	Hunter J K and Scheurle J 1988 Physica D 32 253
[3]	Kaya D and Al-Khaled K 2007 Phys. Lett. A 363 433
[4]	Yuan J M, Shen J and Wu J H 2008 J. Sci. Comput. 34 48
[5]	Hu W P and Deng Z C 2008 Chin. Phys. B 17 3923
[6]	Ceballos J C, Sepúlveda M and Villagrán O P V 2007 Appl. Math. Comput. 190 912
[7]	Bibi N, Tirmizi S I A and Haq S 2011 Appl. Math. 2 608
[8]	Marsden J E, Patrick G W and Shkoller S 1998 Commun. Math. Phys. 199 351
[9]	Bridges T J and Reich S 2001 Phys. Lett. A 284 184
[10]	Reich S 2000 J. Comput. Phys. 157 473
[11]	Chen J B 2004 Chin. Phys. Lett. 21 37
[12]	Hong J L, Liu Y, Munthe-Kaas H and Zanna A 2006 Appl. Numer. Math. 56 814
[13]	Chen J B and Qin M Z 2001 Electr. Trans. Numer. Anal. 12 193
[14]	Wang J 2008 Chin. Phys. Lett. 25 3531
[15]	Ascher U M and Malachlan R I 2004 Appl. Numer. Math. 48 255
[16]	Wang Y S, Wang B and Chen X 2007 Chin. Phys. Lett. 24 312
[17]	Sun Y J and Qin M Z 2004 J. Comput. Math. 22 611
[18]	Kong L H, Hong J L and Zhang J J 2010 J. Comput. Phys. 229 4259
[19]	Cai J X, Yang B and Liang H 2013 Chin. Phys. B 22 030209
[20]	Cai J X, Wang Y S and Qiao Z H 2009 J. Math. Phys. 50 033510
[21]	Chen Y M, Song S H and Zhu H J 2012 Appl. Math. Comput. 218 5552
[22]	Cohen D, Owren B and Raynaud X 2008 J. Comput. Phys. 227 5492
[23]	Wang Y S and Hong J L 2013 Commun. Appl. Math. Comput. 27 163
[24]	Bridges T J and Reich S 2006 J. Phys. A: Math. Gen. 39 5287
[25]	Qin M Z and Wang Y S 2011 Structure-Preserving Algorithms for Partial Differential Equations (Hangzhou: Zhejiang Science and Technology Press) (in Chinese)
[26]	Bridges T J and Derks G 2002 SIAM J. Math. Anal. 33 1356
[27]	Gotay M J 1991 Mechanics, Analysis and Geometry 200 Years after Lagrange (Amsterdam: North Holland) p. 203
[28]	Sirendaoreji 2004 Chaos Soliton. Fract. 19 147

A new explicit multisymplectic integrator for the Kawahara-type equation

A new explicit multisymplectic integrator for the Kawahara-type equation

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