Spatial decay of multi-solitons of the generalized Korteweg-de Vries and nonlinear Schrödinger equations

We study pointwise spatial decay of multi-solitons of the generalized Korteweg-de Vries equations. We obtain that, uniformly in time, these solutions and their derivatives decay exponentially in space on the left of and in the solitons region, and prove rapid decay on the right of the solitons. We a...

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Bibliographic Details
Published in:Mathematische annalen 2023-12, Vol.387 (3-4), p.1163-1198
Main Authors: Côte, Raphaël, Friederich, Xavier
Format: Article
Language:English
Subjects:
Analysis of PDEs
Decay
Mathematical analysis
Mathematics
Mathematics and Statistics
Schrodinger equation
Solitary waves
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Summary:We study pointwise spatial decay of multi-solitons of the generalized Korteweg-de Vries equations. We obtain that, uniformly in time, these solutions and their derivatives decay exponentially in space on the left of and in the solitons region, and prove rapid decay on the right of the solitons. We also prove the corresponding result for multi-solitons of the nonlinear Schrödinger equations, that is, exponential decay in the solitons region and rapid decay outside.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-022-02484-8