Classical and Quantum Mechanical (QM) Effects in the One-Soliton solution of the EM Nonlinear Schrodinger (NLS) Equation

Self-localized Solitons of a q-Deformed Quantum System

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 met…

Nonclassical lattice solitons in optical lattice via Electromagnetically induced transparency

An optical four-level atomic discrete system through optical induction is proposed. A theoretical scheme to produce nonclassical lattice solitons (NLS) in the system is presented with the use of the effects of enhanced self-phase modulation and the giant kerr effect in the electromagnetically induced transparency. The power density and the photon flux can be tuned to a very low level by the controlling field and the soliton can propagate with very slow group velocity. By changing the sign of the detuning $Δ_{1}$, both in-phase and $π$ out-of-phase NLSs can be produced in this system.

From the hypergeometric differential equation to a non linear Schrödinger one

We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation is a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre-Rego Monteiro-Tsallis one.

具有PT对称势的线性耦合NLS方程中孤子的对称破缺分岔与激发

Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials

本文研究具有PT对称势的线性耦合NLS方程中基态和偶极模孤子的对称破缺分岔与稳定性，发现PT对称破缺先于芯间对称破缺，并展示了耗散系统中稳定孤子的存在及孤子形状转换。

Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc.. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrodinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time (PT)-symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex PT-symmetric potentials (e.g., physically releva…

非线性薛定谔方程的共形对偶性：理论及其在参数估计中的应用

Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation

本文建立一维立方-五次方NLSE稳态解与行波解基于交比的共形分类理论，并利用该对称性提出优化后处理方法，提升含噪数据下的参数估计性能。