Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the L² Space

2024/02/25 by Yiling Yang, Yang, Yiling, Engui Fan +3
Mathematics · Physics and Astronomy · #35Q15 #35Q35 #35Q51 #37K15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2402.16222

openalex publication_date 2024/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schrödinger equation under perturbations in L²(ℝ). We demonstrate this stability by utilizing the Bäcklund transformation associated with the Lax pair and by applying the first conservation quantity in L²(ℝ).

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