一类新的2+1维非线性发展方程及其解的对合表示  

A New( 2 + 1)-dimensional Nonlinear Evolution Equation and the Involutive Representations of the Solutions

作　　者：刘亚峰[1] 刘炜[1] 

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043

出　　处：《石家庄铁道大学学报（自然科学版）》2014年第1期106-110,共5页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

摘　　要：由线性谱问题的相容性条件得到一个新的2+1维非线性发展方程。利用位势函数与特征函数之间的约束获得Bargmann系统,通过Euler-Lagrange方程及Legendre变换构造Jacobi-Ostrogradsky坐标。应用Lax对非线性化方法,生成了一个新的有限维Hamilton正则系统。最后证明其为Liouville意义下完全可积系统,并得到发展方程族的对合表示。A new （2 ＋ 1 ） -dimensional nonlinear evolution equation is obtained based on the compatible con- dition of two linear spectral problems. By means of the constraint condition between the potentials and the eigen- vector, the Bargmann system is generated. The Jacobi-Ostrogradsky coordinate system has been found through Euler-Lagrange equation and l_egendre transformations. Using the nonlinearization approach of Lax pairs, a new finite-dimensional Hamilton canonical equations are obtained. Finally, it is proved completely integrable sys- tems, and the involutive solutions of the evolution equations are given.

关 键 词：谱问题 Lax对非线性化 BARGMANN系统 可积系统 对合表示 

分 类 号：O175.9[理学—数学]