Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations

Stefan Le Coz (1) , Tai-Peng Tsai (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UBC - University of British Columbia

We look for solutions to generic nonlinear Schrödinger equations build upon solitons and kinks. Solitons are localized solitary waves and kinks are their non localized counter-parts. We prove the existence of infinite soliton trains, i.e. solutions behaving at large time as the sum of infinitely many solitons. We also show that one can attach a kink at one end of the train. Our proofs proceed by fixed point arguments around the desired profile. We present two approaches leading to different results, one based on a combination of dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.

Mots clés: soliton train; kink-soliton train; multi-soliton; nonlinear Schrödinger equations

Domaines: Equations aux dérivées partielles [math.AP]

Stefan Le Coz, Tai-Peng Tsai. Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations. Nonlinearity, 2014, 27 (11), pp.2689-2709. ⟨hal-00867772⟩