Integrable couplings of soliton equations by perturbations I: A general theory and application to the KDV hierarchy
Integrable couplings of soliton equations by perturbations I: A general theory and application to the KDV hierarchy
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DOI：
10.4310/maa.2000.v7.n1.a2
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发表时间：
1999-12
影响因子：
0.3
通讯作者：
W. Ma
中科院分区：
文献类型：
--
作者：
W. Ma
利用微扰孤子方程的解周围的各种微扰，建立了一个构造孤子方程可积耦合的理论。可以采取多尺度扰动，从而更高维的可积耦合可以呈现。该理论被应用到KdV孤子族。对KdV族中的每一个孤子方程构造了无数个可积耦合，其中包括具有四重Hamilton形式和两类遗传递归算子的可积耦合，以及具有局部2+1维双Hamilton形式和随之而来的2+1维遗传递归算子的可积耦合.
A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale perturbations can be taken and thus higher dimensional integrable couplings can be presented. The theory is applied to the KdV soliton hierarchy. Infinitely many integrable couplings are constructed for each soliton equation in the KdV hierarchy, which contain integrable couplings possessing quadruple Hamiltonian formulations and two classes of hereditary recursion operators, and integrable couplings possessing local 2+1 dimensional bi-Hamiltonian formulations and consequent 2+1 dimensional hereditary recursion operators.