High speed excited multi-solitons in nonlinear Schr\"odinger equations
Analysis of PDEs
2012-04-19 v2
Abstract
We consider the nonlinear Schr\"odinger equation with a general nonlinearity. In dimension higher than 2, this equation admits travelling wave solutions with a fixed profile which is not the ground state. This kind of profiles are called excited states. In this paper, we construct solutions to NLS behaving like a sum of N excited states which spread up quickly as time grows (which we call multi-solitons). We also show that if the flow around one of these excited states is linearly unstable, then the multi-soliton is not unique, and is unstable.
Keywords
Cite
@article{arxiv.1007.3034,
title = {High speed excited multi-solitons in nonlinear Schr\"odinger equations},
author = {Raphaël Cote and Stefan Le Coz},
journal= {arXiv preprint arXiv:1007.3034},
year = {2012}
}