Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy. (English) Zbl 1001.37061

Ma, Wen-Xiu

Methods Appl. Anal. 7, No. 1, 21-55 (2000).

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.

Reviewer: Jan Cholewa (Katowice)

MSC:

37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

soliton equations; integrable couplings; KdV hierarchy