Construction and characterization of solutions converging to solitons for supercritical gKdV equations - Archive ouverte HAL
Article Dans Une Revue Differential and integral equations Année : 2010

Construction and characterization of solutions converging to solitons for supercritical gKdV equations

Résumé

We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such solutions are forced to be exactly solitons by variational characterization, but no such result exists in the supercritical case. In this paper, we first construct a "special solution" in this case by a compactness argument, i.e. a solution which converges to a soliton without being a soliton. Secondly, using a description of the spectrum of the linearized operator around a soliton due to Pego and Weinstein, we construct a one parameter family of special solutions which characterizes all such special solutions.
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Dates et versions

hal-00408104 , version 1 (28-07-2009)
hal-00408104 , version 2 (04-08-2009)

Identifiants

Citer

Vianney Combet. Construction and characterization of solutions converging to solitons for supercritical gKdV equations. Differential and integral equations, 2010, 23 (5-6), pp.513-568. ⟨hal-00408104v2⟩
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