关于AKNS族和一个耦合的MKdV族的规范等价可积系统与<em>r</em>-矩阵

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关于AKNS族和一个耦合的MKdV族的规范等价可积系统与r-矩阵

Department of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, P. R. China

摘要: 得到了一个新的耦合的MKdV族.通过规范变换,首次从AKNS族中得到耦合的MKdV族的Lax表示、可积系与约束流;利用Lax表示,构造了耦合MKdV族的约束流的r-矩阵,同时也给出了该方程族约束流的第二组守恒积分与对合性.
- 规范等价 /
- r-矩阵 /
- 可积系统
Abstract: The new coupled MKdV hierarchy is obtained.By using gauge transformation,the constrained flow,the integrable system and Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarchy and then using the Lax representation the r-matrix for the constrained flow of the coupled MKdV hierarchy was constructed.The second set of conserved integrals of this constrained flow and their involutivity were also given.
- gauge equivalence /
- r-matrix /
- integrable system

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