论文标题
具有非零背景的经典和非局部非线性schrödinger方程的解决方案：双线性和还原方法
The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
论文作者
论文摘要
在本文中，我们开发了一种双线化还原方法，以推导出具有非零背景的经典和非局部非线性schrödinger（NLS）方程。我们从二阶Ablowitz-kaup-newell-segur方程式作为未还原系统开始。使用一对解决方案$（q_0，r_0）$，我们将未还原的系统进行双线化，并根据准双Wronskians获得解决方案。然后，我们通过对Wronskians的列向量引入约束来实现减少，并最终获得还原方程的解决方案，包括经典的NLS方程和具有反向空间，反向时间和反向空间时间的非局部NLS方程。以一组平面波解决方案$（q_0，r_0）$作为背景解决方案，我们为这些列向量提供了明确的公式。作为示例，我们分析并说明了焦点NLS方程和反向空间非本地NLS方程的解决方案。特别是，我们为聚焦NLS方程的任意顺序的胭脂浪潮提供了公式。
In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schrödinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur coupled equations as an unreduced system. With a pair of solutions $(q_0,r_0)$ we bilinearize the unreduced system and obtain solutions in terms of quasi double Wronskians. Then we implement reductions by introducing constraints on the column vectors of the Wronskians and finally obtain solutions to the reduced equations, including the classical NLS equation and the nonlocal NLS equations with reverse-space, reverse-time and reverse-space-time, respectively. With a set of plane wave solution $(q_0,r_0)$ as a background solution, we present explicit formulae for these column vectors. As examples, we analyze and illustrate solutions to the focusing NLS equation and the reverse-space nonlocal NLS equation. In particular, we present formulae for the rouge waves of arbitrary order for the focusing NLS equation.
