Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations
Analysis of PDEs
2009-05-06 v1
Abstract
Multi-soliton solutions, i.e. solutions behaving as the sum of N given solitons as , were constructed in previous works for the L2 critical and subcritical (NLS) and (gKdV) equations. In this paper, we extend the construction of multi-soliton solutions to the L2 supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.
Keywords
Cite
@article{arxiv.0905.0470,
title = {Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations},
author = {Raphael Cote and Yvan Martel and Frank Merle},
journal= {arXiv preprint arXiv:0905.0470},
year = {2009}
}