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Freedom in the expansion and obstacles to integrability in multiple-soliton solutions of the perturbed KdV equation. (English) Zbl 1099.35124

From the summary: The construction of solutions of the perturbed KdV equation encounters obstacles to asymptotic integrability beyond the first order, when the zero-order approximation is not a single-soliton wave. In the standard analysis, the obstacles lead to the loss of integrability of the normal form, resulting in a zero-order term, which does not have the simple structure of the solution of the unperturbed equation. Exploiting the freedom in the perturbative expansion, an algorithm is proposed that shifts the effect of the obstacles from the normal form to the higher-order terms.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K55 Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems
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