Long-Time Asymptotics for the integrable discrete nonlinear Schrödinger equation: The Focusing Case

2015/12/06 by Hideshi Yamane, Yamane, Hideshi · 1 citation
Mathematics · Physics and Astronomy · #35Q15 (Secondary) #35Q55 (Primary) #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1512.01760

openalex publication_date 2015/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schrödinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase shift formulas in different regions. Along rays away from solitons, the behavior of the solution is decaying oscillation. This is one way of stating the soliton resolution conjecture. The proof is based on the nonlinear steepest descent method.

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• Persistence of integrable wave dynamics in the Discrete Gross--Pitaevskii equation: the focusing case

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