具衰减初值的非线性薛定谔方程的长时间渐近性
Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value
摘要：
本文提出了一种新的线上微分非线性薛定谔方程初值问题的Riemann-Hilbert问题形式。我们证明了这个初值问题的解可以从一些相关的Riemann-Hilbert问题的解得到。这一新的DNLS方程的Riemann-Hilbert问题将引导我们使用非线性最速下降/稳相方法或Deift-Zhou方法来推导DNLS方程在直线上的长时间渐近解。
英文摘要：
We present a new Riemann-Hilbert problem formalism for the initial value problem for the derivative nonlinear Schrödinger (DNLS) equation on the line. We show that the solution of this initial value problem can be obtained from the solution of some associated Riemann-Hilbert problem. This new Riemann-Hilbert problem for the DNLS equation will lead us to use nonlinear steepest-descent/stationary phase method or Deift-Zhou method to derive the long-time asymptotic for the DNLS equation on the line.
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