论文标题
Riemann-Hilbert的方法是具有非逐渐呈现边界条件的不均匀五阶非线性schrödinger方程
Riemann-Hilbert approach to the inhomogeneous fifth-order nonlinear Schrödinger equation with non-vanishing boundary conditions
论文作者
论文摘要
我们考虑具有详细的非零边界条件的不均匀的五阶非线性schrödinger（Ifonls）方程。首先，进行了散射问题的光谱分析。首先引入Riemann表面和仿射参数，以将原始光谱参数转换为新参数，以避免多值问题。基于LAX对的IFONLS方程，获得了JOST函数，并系统地建立了它们的分析，渐近，对称特性以及散射矩阵的相应特性。对于逆散射问题，我们讨论了散射系数分别具有简单零和双重零的情况，并进一步得出了相应的精确溶液。此外，当我们为这些精确解决方案选择一些适当的参数时，发现了一些有趣的现象，这有助于研究这些解决方案的传播行为。
We consider the inhomogeneous fifth-order nonlinear Schrödinger (ifoNLS) equation with nonzero boundary condition in detailed. Firstly, the spectral analysis of the scattering problem is carried out. A Riemann surface and affine parameters are first introduced to transform the original spectral parameter to a new parameter in order to avoid the multi-valued problem. Based on Lax pair of the ifoNLS equation, the Jost functions are obtained, and their analytical, asymptotic, symmetric properties, as well as the corresponding properties of the scattering matrix are established systematically. For the inverse scattering problem, we discuss the cases that the scattering coefficients have simple zeros and double zeros, respectively, and we further derive their corresponding exact solutions. Moreover, some interesting phenomena are found when we choose some appropriate parameters for these exact solutions, which is helpful to study the propagation behavior of these solutions.
