Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions

Caroline Kalla (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We present new solutions in terms of elementary functions of the multi-component nonlinear Schrödinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schrödinger equations.

Domaines: Physique mathématique [math-ph]

Caroline Kalla. Breathers and solitons of generalized nonlinear Schrödinger equations as degenerations of algebro-geometric solutions. 2011. ⟨hal-00597964⟩