论文标题
耦合非线性schrödinger方程中孤立波的分叉和光谱稳定性
Bifurcations and Spectral Stability of Solitary Waves in Coupled Nonlinear Schrödinger Equations
论文作者
论文摘要
我们研究了线上耦合的非线性schrödinger方程（CNL）中孤立波的分叉和光谱稳定性。我们假设耦合方程式具有一个解决方案，其中一个组件的零是零，并将其称为$ \ textIt {基本单位波} $。通过使用其中一位作者及其合作者的结果，检测到基本孤独波的分叉。我们利用汉密尔顿 - 克雷因指数理论和埃文斯功能技术来确定分叉孤立波的光谱或轨道稳定性以及在某些非排定条件下易于验证的基本条件下的光谱或轨道稳定性，与先前的结果相比。我们将理论应用于具有立方非线性的CNL，并为理论结果提供了数值证据。
We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrödinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a $\textit{fundamental solitary wave}$. By using a result of one of the authors and his collaborator, the bifurcations of the fundamental solitary wave are detected. We utilize the Hamiltonian-Krein index theory and Evans function technique to determine the spectral or orbital stability of the bifurcated solitary waves as well as as that of the fundamental one under some nondegenerate conditions which are easy to verify, compared with those of the previous results. We apply our theory to CNLS with a cubic nonlinearity and give numerical evidences for the theoretical results.
