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应用数学学报  1993, Vol. 16 Issue (4): 477-481    DOI:
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导数非线性Schrödinger方程族解的表示
顾祝全
石家庄铁道学院基础部, 石家庄 050043
THE REPRESENTATIONS OF SOLUTIONS OF THE DNLS HIERARCHY
GU ZHU-QUAN
Department of Basic Courses, Shijiazhuang Railway Institute, Shijiazhuang 050043
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摘要 由Liouville意义下的完全可积系[1]的对合解产生孤子方程的解的对合表示[2],为求解孤子方程以及讨论解的性质提供了新的途径.
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顾祝全
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Abstract: 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 integrable system. Therefore, the solutions of the DNLS hierarchy are given by the involutivesolutions through constraint relations.
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收稿日期: 1990-04-05;
引用本文:   
顾祝全. 导数非线性Schrödinger方程族解的表示[J]. 应用数学学报, 1993, 16(4): 477-481.
GU ZHU-QUAN. THE REPRESENTATIONS OF SOLUTIONS OF THE DNLS HIERARCHY[J]. Acta Mathematicae Applicatae Sinica, 1993, 16(4): 477-481.
 
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