中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70205-070205.doi: 10.1088/1674-1056/21/7/070205
何国亮a b, 耿献国a
He Guo-Liang(何国亮)a)b)† and Geng Xian-Guo(耿献国)a)
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.
中图分类号: (Integrable systems)