Construction and characterization of solutions converging to solitons for supercritical gKdV equations - Mathematics > Analysis of PDEsReport as inadecuate




Construction and characterization of solutions converging to solitons for supercritical gKdV equations - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider the generalized Korteweg-de Vries equation in the supercriticalcase, and we are interested in solutions which converge to a soliton in largetime in H^1. In the subcritical case, such solutions are forced to be exactlysolitons by variational characterization, but no such result exists in thesupercritical case. In this paper, we first construct a -special solution- inthis case by a compactness argument, i.e. a solution which converges to asoliton without being a soliton. Secondly, using a description of the spectrumof the linearized operator around a soliton due to Pego and Weinstein, weconstruct a one parameter family of special solutions which characterizes allsuch special solutions.



Author: Vianney Combet LM-Versailles

Source: https://arxiv.org/



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