Coupled system description of perturbed KdV equation

Details Coupled system description of perturbed KdV equation Coupled system description of perturbed KdV equation

2008-05-28

arxiv.org/abs/0805.4281v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations: The (inte-grable) Normal Form for KdV-type solitons, which obey the usual infinity of KdV-conservation laws, and an auxiliary equation that describes the contribution of obstacles to asymptotic inte-grability, which arise from the second order onwards. The analysis has been carried through the third order in the expansion. Within that order, the solution of the auxiliary equation is a con-served quantity.

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