Open AccessInstability of the soliton for the focusing, mass-critical generalized KdV equation
Author(s) -
Benjamin Dodson,
Cristian Gavrus
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021171
Subject(s) - korteweg–de vries equation , soliton , mathematical physics , instability , physics , dissipative soliton , norm (philosophy) , mathematics , quantum mechanics , nonlinear system , law , political science
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 \begin{document}$ L^{2} $\end{document} norm must eventually move away from the soliton.