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Zbl 1001.37061
Ma, Wen-Xiu
Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy. (English)
[J] Methods Appl. Anal. 7, No.1, 21-55 (2000). ISSN 1073-2772

The author discusses a problem of integrable couplings. That is, having an integrable system of evolution equations $u_t=K(u)$, how to obtain a bigger (nontrivial) integrable system consisting of $u_t=K(u)$ and $v_t = S(u,v)$. ``Using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter" the author developes ``a theory for constructing integrable couplings of soliton equations". Application of the theory to the KdV hierarchy is given.
[Jan Cholewa (Katowice)]

MSC 2000:: *37K10 Completely integrable systems etc.
37K40 Soliton theory, asymptotic behavior of solutions
35Q53 KdV-like equations

Keywords: soliton equations; integrable couplings; KdV hierarchy

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