An extension of the modified Sawada–Kotera equation and conservation laws

doi:10.1088/1674-1056/21/7/070205

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70205-070205.doi: 10.1088/1674-1056/21/7/070205

An extension of the modified Sawada–Kotera equation and conservation laws

何国亮^{a b}, 耿献国^a

a Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China;
b Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China

收稿日期:2011-11-07 修回日期:2012-02-17 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171312) and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 200804590008).

An extension of the modified Sawada–Kotera equation and conservation laws

He Guo-Liang(何国亮)^a)b)† and Geng Xian-Guo(耿献国)^a)

a Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China;
b Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China

Received:2011-11-07 Revised:2012-02-17 Online:2012-06-01 Published:2012-06-01
Contact: Geng Xian-Guo E-mail:glhemath@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171312) and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No. 200804590008).

摘要/Abstract

摘要： Based on the modified Sawada--Kotera equation, we introduce a 3?3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawada--Kotera equation, by which a Lax pair of the modified Sawada--Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawada--Kotera equation, the Kaup--Kupershmidt equation, and the modified Sawada--Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada--Kotera equation are constructed with the aid of their Lax pairs.

关键词: spectral problem, explicit solutions, conservation laws

Abstract: Based on the modified Sawada--Kotera equation, we introduce a 3?3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawada--Kotera equation, by which a Lax pair of the modified Sawada--Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawada--Kotera equation, the Kaup--Kupershmidt equation, and the modified Sawada--Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada--Kotera equation are constructed with the aid of their Lax pairs.

Key words: spectral problem, explicit solutions, conservation laws

中图分类号: (Integrable systems)

02.30.Ik

02.30.Jr (Partial differential equations)

何国亮, 耿献国. An extension of the modified Sawada–Kotera equation and conservation laws[J]. 中国物理B, 2012, 21(7): 70205-070205.

He Guo-Liang(何国亮) and Geng Xian-Guo(耿献国) . An extension of the modified Sawada–Kotera equation and conservation laws[J]. Chin. Phys. B, 2012, 21(7): 70205-070205.

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An extension of the modified Sawada–Kotera equation and conservation laws

An extension of the modified Sawada–Kotera equation and conservation laws

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