Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation

doi:10.1088/1674-1056/23/1/010203

Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 10203-010203.doi: 10.1088/1674-1056/23/1/010203

Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation

辛祥鹏, 苗倩, 陈勇

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

收稿日期:2013-05-15 修回日期:2013-06-07 出版日期:2013-11-12 发布日期:2013-11-12
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the National High Technology Research and Development Program of China (Grant No. 2011AA010101), and the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213).

Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation

Xin Xiang-Peng (辛祥鹏), Miao Qian (苗倩), Chen Yong (陈勇)

Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China

Received:2013-05-15 Revised:2013-06-07 Online:2013-11-12 Published:2013-11-12
Contact: Chen Yong E-mail:ychen@sei.ecnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11075055 and 11275072), the Innovative Research Team Program of the National Natural Science Foundation of China (Grant No. 61021004), the National High Technology Research and Development Program of China (Grant No. 2011AA010101), and the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213).

摘要/Abstract

摘要： The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.

关键词: nonlocal symmetry, optimal system, prolonged system, explicit solutions

Abstract: The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.

Key words: nonlocal symmetry, optimal system, prolonged system, explicit solutions

中图分类号: (Partial differential equations)

02.30.Jr

11.10.Lm (Nonlinear or nonlocal theories and models) 02.20.-a (Group theory) 04.20.Jb (Exact solutions)

辛祥鹏, 苗倩, 陈勇. Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation[J]. Chin. Phys. B, 2014, 23(1): 10203-010203.

Xin Xiang-Peng (辛祥鹏), Miao Qian (苗倩), Chen Yong (陈勇). Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation[J]. Chin. Phys. B, 2014, 23(1): 10203-010203.

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Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation

Nonlocal symmetry, optimal systems, and explicit solutions of the mKdV equation

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