灰孤立子背景的精确Bogoliubov-de Gennes解
Exact Bogoliubov-de Gennes Solutions for Grey Soliton Backgrounds
摘要：
我们导出并讨论了一维Bogoliubov-de Gennes方程在三次非线性薛定谔方程的一般灰孤子解附近的小振幅激发下的完整精确解.我们的结果扩展了先前已知的静止暗孤子背景的情况。我们推导出我们的非零频率的解决方案，使用一个变种的薛定谔方程的无反射电位的因式分解方法。我们还详细讨论了零模解。
英文摘要：
We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small amplitude excitations around general grey soliton solutions to the cubic nonlinear Schrödinger equation. Our results extend the previously known case of the motionless dark soliton background. We derive our non-zero frequency solutions using a variant of the factorization method for Schrödinger equations with reflectionless potentials. We also discuss the zero mode solutions at length.
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