导数非线性Schrdinger方程族解的表示  

THE REPRESENTATIONS OF SOLUTIONS OF THE DNLS HIERARCHY

作　　者：顾祝全[1] 

机构地区：[1]石家庄铁道学院基础部

出　　处：《应用数学学报》1993年第4期477-481,共5页Acta Mathematicae Applicatae Sinica

摘　　要：The solutions of soliton systems are generated by using involutive solutions of the Liou-ville completely integrable system, which provides a new way for solving soliton equations.The complex forms (of symplectic structure and Poisson bracket and Hamiltonian canonicalequation) are deduced through appropriate transformation, by using the real symplecticstructure and real Poisson bracket and real Hamiltonian canonical equation. Hence it isfurther proved that the nonlinearized Lax presentations of two classes of DNLS hierarchiesbecome exactly the complex Hamiltonian canonical equations in the Liouville completely in-tegrable system. Therefore, the solutions of the DNLS hierarchy are given by the involutivesolutions through constraint relations.The solutions of soliton systems are generated by using involutive solutions of the Liou-ville completely integrable system, which provides a new way for solving soliton equations.The complex forms (of symplectic structure and Poisson bracket and Hamiltonian canonicalequation) are deduced through appropriate transformation, by using the real symplecticstructure and real Poisson bracket and real Hamiltonian canonical equation. Hence it isfurther proved that the nonlinearized Lax presentations of two classes of DNLS hierarchiesbecome exactly the complex Hamiltonian canonical equations in the Liouville completely in-tegrable system. Therefore, the solutions of the DNLS hierarchy are given by the involutivesolutions through constraint relations.

关 键 词：薛定谔方程 解 非线性 发展方程 

分 类 号：O157.2[理学—数学]