The Gerdjikov-Ivanov-type derivative nonlinear Schrödinger equation: long-time dynamics of nonzero boundary conditions
The Gerdjikov-Ivanov-type derivative nonlinear Schrödinger equation: long-time dynamics of nonzero boundary conditions
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Gerdjikov-Ivanov 型导数非线性薛定谔方程：非零边界条件的长期动力学
DOI：
10.1002/mma.5698
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Liu Nan
中科院分区：
文献类型：
--
作者：
Guo Boling;Liu Nan
考虑Gerdjikov-Ivanov型导数非线性薛定谔方程 在线上给定初始值eq（x，0），并且满足无穷远处的对称非零边界条件，即q（x，0）→q±asx→±∞，并且|q±| =q0>0。本文的目的是研究这类初值问题ast→∞解的渐近性态。主要工具是通过使用最速下降法和所谓的g函数机制对关联矩阵Riemann‐Hilbert问题进行渐近分析。我们证明了这个初值问题的解q（x，t）在下平面的不同区域有不同的渐近行为。在各区域 并且，该解采用平面波的形式。在该区域中，解的形式为调制椭圆波。
We consider the Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation on the line. The initial valueq(x,0) is given and satisfies the symmetric, nonzero boundary conditions at infinity, that is,q(x,0)→q±asx→±∞, and |q±|=q0>0. The goal of this paper is to study the asymptotic behavior of the solution of this initial value problem ast→∞. The main tool is the asymptotic analysis of an associated matrix Riemann‐Hilbert problem by using the steepest descent method and the so‐calledg‐function mechanism. We show that the solutionq(x,t) of this initial value problem has a different asymptotic behavior in different regions of thext‐plane. In the regions and , the solution takes the form of a plane wave. In the region , the solution takes the form of a modulated elliptic wave.