非傍轴非线性薛定谔方程的可积性与孤立波动力学
On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves
摘要：
采用Painlevé奇异结构分析方法，研究了描述超宽非傍轴光束在平面光波导中传输的非傍轴非线性薛定谔（NNLS）方程的可积性.我们的研究表明，NNLS方程不满足Painlevé检验。然而，我们构造了一个明亮的孤立波解的NNLS方程使用Hirota的直接方法。此外，我们数值证明了所获得的明亮的孤立波的稳定传播，即使在存在外部扰动的形式的白噪声。然后，我们数值研究了两个和三个明亮的孤立波的相干相互作用动力学。我们的研究揭示了有趣的能量切换碰撞孤立波由于非傍轴性。
英文摘要：
The integrability nature of a nonparaxial nonlinear Schrödinger (NNLS) equation, describing the propagation of ultra-broad nonparaxial beams in a planar optical waveguide, is studied by employing the Painlevé singularity structure analysis. Our study shows that the NNLS equation fails to satisfy the Painlevé test. Nevertheless, we construct one bright solitary wave solution for the NNLS equation by using the Hirota's direct method. Also, we numerically demonstrate the stable propagation of the obtained bright solitary waves even in the presence of an external perturbation in a form of white noise. We then numerically investigate the coherent interaction dynamics of two and three bright solitary waves. Our study reveals interesting energy switching among the colliding solitary waves due to the nonparaxiality.
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