Construction of Multi-solitons for a Generalized Derivative Nonlinear Schrödinger Equation

We consider a derivative nonlinear Schrödinger equation with general nonlinearlity: i ∂ t u + ∂ x 2 u + i | u | 2 σ ∂ x u = 0 , In Tang and Xu (J Differ Equ 264(6):4094–4135, 2018), the authors prove the stability of two solitary waves in energy space for σ ∈ ( 1 , 2 ) . As a consequence, there exists a solution of the above equation which is close arbitrary to sum of two solitons in energy space when σ ∈ ( 1 , 2 ) . Our goal in this paper is proving the existence of multi-solitons in energy space for σ ⩾ 3 2 . Our proofs proceed by fixed point arguments around the desired profile, using Strichartz estimates.