可积离散非线性Schrödinger方程的长时间渐近性:聚焦情况

Pub Date : 2015-12-06 DOI:10.1619/FESI.62.227

H. Yamane

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引用次数: 4

摘要

研究了聚焦可积离散非线性Schr\ odinger方程的长时间渐近性。在初值的一般假设下，解渐近是1孤子的和。我们在不同的区域得到了不同的相移公式。沿着远离孤子的射线，溶液的行为是衰减振荡。这是说明孤子解析猜想的一种方法。该证明基于非线性最陡下降法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Long-time Asymptotics for the Integrable Discrete Nonlinear Schrödinger Equation: the Focusing Case

We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schr\"odinger 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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