变系数修正非线性薛定谔方程中超短暗孤子相互作用和非线性隧穿
Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficients
摘要：
利用变系数修正的非线性薛定谔方程（Vc-MNLSE）研究了非均匀光纤中的暗孤子动力学行为。利用Hirota双线性（HB）方法研究了超短暗孤子脉冲的演化和相互作用。特别是，我们给了很多洞察的自陡峭（SS）的暗孤子动力学的影响。该研究揭示了冲击波的形成，作为SS的主要影响。数值研究了连续波背景下暗孤子的传输，并在存在光子噪声的情况下检验了孤子解的稳定性。通过渐近分析讨论了暗孤子的弹性碰撞行为。另一方面，考虑暗孤子通过势垒/阱的非线性隧穿，我们发现暗孤子的隧穿依赖于势垒的高度和孤子的振幅。隧穿孤子的强度要么形成一个峰，要么形成一个谷，并在隧穿后保持其形状。对于指数背景，孤子在隧穿势垒/阱后有压缩的趋势。
英文摘要：
We present the study of the dark soliton dynamics in an inhomogenous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.
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