High speed excited multi-solitons in nonlinear Schrödinger equations

Details High speed excited multi-solitons in nonlinear Schrödinger equations High speed excited multi-solitons in nonlinear Schrödinger equations

2010-07-18

arxiv.org/abs/1007.3034v2

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.matpur.2011.03.004

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.

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