论文标题
与抗 - $ \ Mathcal {pt} $对称性相关的非线性schrödinger方程的孤立波的行为
Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with anti-$\mathcal{PT}$ symmetry
论文作者
论文摘要
我们讨论了1+1个维度的非线性两个组件非线性schrödinger系统的移动和捕获孤立波解决方案对抗 - $ \ Mathcal {pt} $外部周期性复杂电位的响应。通过进行非线性系统的数值模拟并使用集体坐标变分近似来探索受干扰孤立波的动力学行为。我们提出了与其中涉及的参数和初始条件的选择相对应的案例示例。将集体坐标近似值的结果与数值模拟进行了比较，在这些模拟中，我们观察到两者之间的质量一致性。与复杂的周期性$ \ Mathcal {pt} $ - 对称电位中的单一组分孤立波的情况不同，集体坐标方程没有较小的振荡状态，最初，两个组件的高度在相反方向上通常会导致不稳定。我们发现，我们在单一组件情况下使用的动态稳定性标准被证明是当前设置中动态不稳定性的良好指标。
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schrödinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of the parameters and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic $\mathcal{PT}$-symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case is proven to be a good indicator for the onset of dynamic instabilities in the present setup.
