Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations

Raphaël Côte (1) , Yvan Martel (2) , Frank Merle (3, 4)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LMV - Laboratoire de Mathématiques de Versailles
3 IHES - Institut des Hautes Études Scientifiques
4 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

Multi-soliton solutions, i.e. solutions behaving as the sum of N given solitons as $t\to +\infty$, were constructed in previous works for the L2 critical and subcritical (NLS) and (gKdV) equations. In this paper, we extend the construction of multi-soliton solutions to the L2 supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.

Domaines: Equations aux dérivées partielles [math.AP]

Raphaël Côte, Yvan Martel, Frank Merle. Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations. Revista Matemática Iberoamericana, 2011, 27 (1), pp.273-302. ⟨10.4171/RMI/636⟩. ⟨hal-00385072⟩