English

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 t+t\to +\infty, 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}
}