Construction and characterization of solutions converging to solitons for supercritical gKdV equations
Abstract
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.
Keywords
Cite
@article{arxiv.0907.5486,
title = {Construction and characterization of solutions converging to solitons for supercritical gKdV equations},
author = {Vianney Combet},
journal= {arXiv preprint arXiv:0907.5486},
year = {2009}
}
Comments
38 pages ; submitted ; v2: margins modified