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arXiv 1702.02084nlin.SImath.AP
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半直线上微分非线性薛定谔方程的长时间渐近性

Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line

L. K. Arruda, J. Lenells

摘要:

在初始值和边值属于Schwartz类的假设下,我们得到了半直线上的非线性薛定谔方程解的渐近公式.这些公式清楚地表明了边界对解的影响。该方法是基于一个相关的黎曼-希尔伯特问题的非线性最速下降分析。

英文摘要:

We derive asymptotic formulas for the solution of the derivative nonlinear Schrödinger equation on the half-line under the assumption that the initial and boundary values lie in the Schwartz class. The formulas clearly show the effect of the boundary on the solution. The approach is based on a nonlinear steepest descent analysis of an associated Riemann-Hilbert problem.

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