具有Pöschl-Teller势阱和方势阱的非线性薛定谔方程的束缚态谱
Bound states spectrum of the nonlinear Schrödinger equation with Pöschl-Teller and square potential wells
摘要：
我们得到了非线性薛定谔方程中修正的Pöschl-Teller势阱和方势阱的束缚态谱。对于一个固定的规范的束缚态，这两个潜在的频谱原来是由有限数量的多节点局域化状态。我们使用调制不稳定性分析，推导出的关系，给出了可能的本地化状态的数量和节点的最大数量的潜在的宽度。这两个势的孤子散射证实了局域态的存在，形成的陷阱模式。量子反射的临界速度计算使用被困模式的能量。
英文摘要：
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.
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