Artículo de revista
Nonlinear stability of 2-solitons of the sine-Gordon equation in the energy space
Fecha
2019Registro en:
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Volumen 36, Issue 4, 2019, Pages 977-1034
02941449
10.1016/j.anihpc.2018.10.005
Autor
Muñoz, Claudio
Palacios, José M.
Institución
Resumen
© 2018 Elsevier Masson SASIn this article we prove that 2-soliton solutions of the sine-Gordon equation (SG) are orbitally stable in the natural energy space of the problem H1×L2. The solutions that we study are the 2-kink, kink–antikink and breather of SG. In order to prove this result, we will use Bäcklund transformations implemented by the Implicit Function Theorem. These transformations will allow us to reduce the stability of the three solutions to the case of the vacuum solution, in the spirit of previous results by Alejo and the first author [3], which was done for the case of the scalar modified Korteweg–de Vries equation. However, we will see that SG presents several difficulties because of its vector valued character. Our results improve those in [5], and give the first rigorous proof of the nonlinear stability in the energy space of the SG 2-solitons.