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Pré-Publication, Document De Travail Année : 2021

Construction of the multi-soliton trains for a generalized derivative nonlinear Schr\"odinger equations by a fixed point method

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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Dates et versions

hal-03230989 , version 1 (20-05-2021)
hal-03230989 , version 2 (14-10-2021)
hal-03230989 , version 3 (21-03-2022)

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Citer

Phan van Tin. Construction of the multi-soliton trains for a generalized derivative nonlinear Schr\"odinger equations by a fixed point method. 2021. ⟨hal-03230989v2⟩
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