The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrodinger equation

Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential

We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger (FNLS) equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole (antisymmetry) and tripo…

Quantum versus classical effects in the chirped-drive discrete nonlinear Schrodinger equation

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous classical-like nonlinear phase-locking (autoresonance). Two-level arguments are used to study the ladder-climbing process, and semiclassical theory describes the autoresonance effect. The regimes of efficient excitation in the problem are identified and characterized in terms of three dimensionless parameters describing the driving strength, the dispersion nonlinearit…

Dynamical chaos in nonlinear Schrödinger models with subquadratic power nonlinearity

We devise an analytical method to deal with a class of nonlinear Schrödinger lattices with random potential and subquadratic power nonlinearity. An iteration algorithm is proposed based on multinomial theorem, using Diophantine equations and a mapping procedure onto a Cayley graph. Based on this algorithm, we were able to obtain several hard results pertaining to asymptotic spreading of the nonlinear field beyond a perturbation theory approach. In particular, we show that the spreading process is subdiffusive and has complex microscopic organization involving both long-time trapping phenomena …

Solitons in a nonlinear Schrodinger equation with PT-symmetric potentials and inhomogeneous nonlinearity: stability and excitation of nonlinear modes

We report branches of explicit expressions for nonlinear modes in parity-time (PT) symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even when the PT-symmetry of respective underlying linear models is broken. Based on the examples of these solutions we describe an algorithm of excitation of a stable nonlinear mode in a model, whose linear limit is unstable. The method is based on the adiabatic change of the control parameter driving the mode along a branch bifurcating from a stable linear mode. T…

Anderson localization in the quintic nonlinear Schrödinger equation

In the present paper we consider the quintic defocusing nonlinear Schrödinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The main result shows that Anderson localization requires a cutoff on the value of the parameter which controls the quintic nonlinearity, with the cutoff depending on the amplitude of the random potential.

一维非线性薛定谔方程小解的高阶长时间渐进行为

High-order long-time asymptotics for small solutions to the one-dimensional nonlinear Schrödinger equation

本文研究了一维非线性薛定谔方程小解的长时间渐进行为，利用时空共振方法推导了任意阶渐进行为，考虑了非线性立方项的远场效应。