一个类似于KN族的可积系及其可积耦合

An Integrable System Similar to the KN Hierarchy andIts Integrable Coupling

中文关键词:  可积系  loop代数A₁  等谱问题  可积耦合

英文关键词:integrable system  loop algebra A₁  isospectral problem  integrable coupling.

中文摘要:

      本文选用loop代数A₁的一个子代数,建立了一个线笥等谱问题,导出了一个类似KN族的可积方程族．通过建立求可积耦合的一种简便直接方法,求出了该方程族的可积耦合．这种方法也适用于其它方程族。

英文摘要:

      A linear isospectral problem is established by choosing a subalgebra of loop alge-bra A₁, from which an integrable hierarchy of equations similar to the KN hierarchy is de-rived. A simple straightforward method for obtaining integrable couplings is proposed. Itfollows that the integrable coupling of the above hierarchy is obtained. This method can beused generally.