Construction of the multi-solitons for a generalized derivative nonlinear Schr\"odinger equation
Résumé
We consider a derivative nonlinear Schrödinger equation with general nonlinearlity: i∂tu + ∂ 2 x u + i|u| 2σ ∂xu = 0, In [12], the authors prove the stability of two solitary waves in energy space for σ ∈ (1, 2). As a consequence, there exists a two-soliton trains in energy space for σ ∈ (1, 2). Our goal in this paper is proving the existence of multi-soliton trains in energy space for σ 5 2. Our proofs proceed by xed point arguments around the desired prole, using Strichartz estimates.
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