Lie Symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities

Peregrine comb: multiple compression points for Peregrine rogue waves in periodically modulated nonlinear Schr{ö}dinger equations

It is shown that sufficiently large periodic modulations in the coefficients of a nonlinear Schr{ö}dinger equation can drastically impact the spatial shape of the Peregrine soliton solutions: they can develop multiple compression points of the same amplitude, rather than only a single one, as in the spatially homogeneous focusing nonlinear Schr{ö}dinger equation. The additional compression points are generated in pairs forming a comb-like structure. The number of additional pairs depends on the amplitude of the modulation but not on its wavelength, which controls their separation distance. The…

Perturbation theory for the modified nonlinear Schr{ö}dinger solitons

The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schr{ö}dinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed analysis of the adiabatic approximation to perturbation-induced evolution of the soliton parameters is given. The linear perturbation and the Raman gain are considered as examples.

一维非线性薛定谔方程远离平衡态的表征

Characterizing far from equilibrium states of the one-dimensional nonlinear Schr{ö}dinger equation

本文利用逆散射变换提出一种识别Lax谱离散特征值的简单方法，用于定量表征一维散焦非线性薛定谔方程远离平衡态中的孤子数量与速度分布。