Global existence for the derivative NLS equation in the presence of solitons

2017/03/31 by Aaron Saalmann, Saalmann, Aaron · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1704.00071

openalex publication_date 2017/03/31 · openalex created_date 2017/08/31 · openalex updated_date 2026/07/28

Abstract

We prove the existence of global solutions to the DNLS equation with initial data in a large subset of H²(\mathbb R)∩ H^1,1(\mathbb R) containing a neighborhood of all solitons. We use the inverse scattering transform method, which was recently developed by D. Pelinovsky and Y. Shimabukuro, and an auto-Bäcklund transform in order to include solitons.

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