论文标题
具有Pöschl-Teller和Square势井的非线性Schrödinger方程的结合状态光谱
Bound states spectrum of the nonlinear Schrödinger equation with Pöschl-Teller and square potential wells
论文作者
论文摘要
我们在非线性Schrödinger方程中获得了修改的PöschlTeller和平方电位井的结合状态光谱。对于固定状态的固定标准，两个电势的光谱都由有限数量的多节点局部状态组成。我们使用模量不稳定性分析来得出根据电位宽度来提供可能的局部状态数量和最大节点数量的关系。这两个电势的孤子散射证实了形成为被困模式的局部状态的存在。使用被困模式的能量计算量子反射的临界速度。
We obtain the spectrum of bound states for a modified Pöschl-Teller and square potential wells in the nonlinear Schrödinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite number of multi-node localized states. We use modulational instability analysis to derive the relation that gives the number of possible localized states and the maximum number of nodes in terms of the width of the potential. Soliton scattering by these two potentials confirmed the existence of the localized states which form as trapped modes. Critical speed for quantum reflection was calculated using the energies of the trapped modes.
