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

Benjamin Dodson | Zendy; Cristian Gavrus | Zendy

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

Author(s) -

Benjamin Dodson,

Cristian Gavrus

Publication year - 2021

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.

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