一类非线性演化方程族的可积耦合

Integrable Couplings of a Type of Nonlinear Evolution Equations

寻求孤立子理论中的可积系统是可积系理论中的一个重要研究课题 ,其一般模式是现行的屠规彰格式。但寻求耦合系统的可积性问题 ,也仅是由马文秀博士研究的一个孤立子方程的可积耦合 ,对于一族孤立子方程的可积耦合目前尚未研究。本文通过构造一个新的 Loop代数 G和作一个恰当的 Lax对变换 ,得到了一类非线性演化方程族的可积耦合。作为例子说明 ,本文求得了一类 AKNS(4个人名字 :Ablowitz,Kaup,Newell,Segur)

Seeking for integrable systems in soliton theory is an important topic of integrable system theory. Its general pattern is the carrent Tu Guizhang′s model. However, the study of integration of coupled system is only the integrable coupling of only one equation due to Doctor Ma Wenxiu. The integrable couplings of a family of solitary equations can not by far be considered at present. In this paper, a new loop algebra and a suitable transformation of Lax pair are constructed, for which integrable couplings of a kind of nonlineor evolution equations are obtained .As an illustrative example, the integrable coupling of a type of generalized AKNS(The shortened form of four people s name: Ablowitz,Kaup,Newell,Segur) hierarchy of equations is presented.