论文标题
$ \ Mathcal {pt} $和超对称潜力的耦合非线性schrödinger方程的被困的孤立波解的稳定性和响应
Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential
论文作者
论文摘要
我们向$ 1 $+$ 1 $ 1 $尺寸的耦合非线性Schrödinger系统的孤独波解在存在外部，超对称和复杂的$ \ mathcal {pt} $ - 对称潜力的情况下。 Schrödinger系统这项工作着重于具有通过分析和数值方法研究的存在，稳定性和时空动力学的精确解决方案。考虑到以八个和十二个时间依赖性的集体坐标探索孤立波的稳定性和动力学的两个不同的近似值。我们发现集体坐标近似中较小的振荡频率的特定潜在选择以及分析表达式的稳定区域。通过对非线性Schrödinger系统进行系统的数值模拟，我们的发现得到了进一步支持。
We present trapped solitary wave solutions of a coupled nonlinear Schrödinger system in $1$+$1$ dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates. We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the collective coordinate approximation. Our findings are further supported by performing systematic numerical simulations of the nonlinear Schrödinger system.
