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We look for solutions to general nonlinear Schrodinger equations built 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 Lp − Lp' dispersive estimates and Strichartz estimates, the other based only on Strichartz estimates.

Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations