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

被引：6
作者：
He, Guo-Liang [1 ,2 ]
Geng, Xian-Guo [1 ]
机构：
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Peoples R China
[2] Zhengzhou Univ Light Ind, Dept Math & Informat Sci, Zhengzhou 450002, Peoples R China
来源：
CHINESE PHYSICS B | 2012年 / 21卷 / 07期
基金：
中国国家自然科学基金;
关键词：
spectral problem; explicit solutions; conservation laws;
D O I：
10.1088/1674-1056/21/7/070205
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Based on the modified Sawada-Kotera equation, we introduce a 3 x 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.
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页数：6
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