论文标题
Q变形量子系统的自定位孤子
Self-localized Solitons of a q-Deformed Quantum System
论文作者
论文摘要
除了纯粹的数学兴趣之外，Q的信息对于各种物理现象的建模和解释都是有希望的。在本文中，我们从数值上研究了具有Q变形的Rosen-Morse电位的非线性Schrödinger方程（NLSE）的自定位的孤子解（NLSE）的存在和特性。通过实施PETVIASHVILI方法（PM），我们获得了NLSE的自定位的一个和两个soliton溶液，具有Q呈现的Rosen-Morse电位。为了调查这些孤子的时间行为和稳定性，我们使用$ 4^{th} $ order runge-kutta time集成符实现了傅立叶光谱方法。我们观察到，自定位的一个和两个孤子稳定，并保持脉动行为和孤子波形的旁b的脉动行为和较小的变化。此外，我们研究了这些孤子在嘈杂的扰动下的稳定性和鲁棒性。在NLSE的框架内建模的正弦单色波场，其Q形成Q的Rosen-Morse电位变成了混乱的波场，并由于噪声触发的调节不稳定性而表现出流氓振荡，但是，NLSE的自由度化的Solitons具有强大的Rosen-Morse潜能，并具有稳定的噪音。我们还表明，在使用Savitzky-Golay滤波器执行的DeNoising过程后，可以重建孤子配置文件。
Beyond a pure mathematical interest, q-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a q-deformed Rosen-Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized one and two soliton solutions of the NLSE with a q-deformed Rosen-Morse potential. In order to investigate the temporal behavior and stabilities of these solitons, we implement a Fourier spectral method with a $4^{th}$ order Runge-Kutta time integrator. We observe that the self-localized one and two solitons are stable and remain bounded with a pulsating behavior and minor changes in the sidelobes of the soliton waveform. Additionally, we investigate the stability and robustness of these solitons under noisy perturbations. A sinusoidal monochromatic wave field modeled within the frame of the NLSE with a q-deformed Rosen-Morse potential turns into a chaotic wavefield and exhibits rogue oscillations due to modulation instability triggered by noise, however, the self-localized solitons of the NLSE with a q-deformed Rosen-Morse potential are stable and robust under the effect of noise. We also show that soliton profiles can be reconstructed after a denoising process performed using a Savitzky-Golay filter.
