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Chin. Phys. B, 2012, Vol. 21(7): 070205    DOI: 10.1088/1674-1056/21/7/070205
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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
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.
Keywords:  spectral problem      explicit solutions      conservation laws  
Received:  07 November 2011      Revised:  17 February 2012      Accepted manuscript online: 
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
Fund: 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).
Corresponding Authors:  Geng Xian-Guo     E-mail:

Cite this article: 

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

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