Instability of the soliton for the focusing, mass-critical generalized KdV equation

Benjamin Dodson; Cristian Gavrus

doi:10.3934/dcds.2021171

Article Contents

2022, Volume 42, Issue 4: 1767-1799. Doi: 10.3934/dcds.2021171

This issue Previous Article Nonlinear nonlocal reaction-diffusion problem with local reaction Next Article Multiplicity of closed Reeb orbits on dynamically convex

$ \mathbb{R}P^{2n-1} $

for

$ n\geq2 $

Instability of the soliton for the focusing, mass-critical generalized KdV equation

Benjamin Dodson and
Cristian Gavrus

Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

Received: March 2021

Early access: November 2021

Published: April 2022

The first author acknowledges the support of NSF grant DMS-1764358

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Abstract

In this paper we prove instability of the soliton for the focusing, mass-critical generalized KdV equation. We prove that the solution to the generalized KdV equation for any initial data with mass smaller than the mass of the soliton and close to the soliton in $ L^{2} $ norm must eventually move away from the soliton.

Keywords:

KdV.

Mathematics Subject Classification: 35Q53.

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References

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