Periodic and solitary waves of the cubic–quintic nonlinear Schrödinger equation

Abstract

This paper presents the possible periodic solutions and the solitons of the cubic–quintic nonlinear Schrödinger equation. Corresponding to five types of different structures of the pseudo-potentials, five types of periodic solutions are given explicitly. Five types of solitons are also obtained explicitly from the limiting procedures of the periodic solutions. This will benefit the study of the generation of fast ions or electrons, which are produced from the soliton breaking when the plasma is irradiated a high-intensity laser pulse.

Diverging probability-density functions for flat-top solitary waves

“…The CQNLSE is a simple nonintegrable extension of the cubic nonlinear Schrödinger equation (CNLSE) possessing solitary wave solutions. The CQNLSE describes a variety of physical systems including pulse propagation in semiconductor-doped optical fibers [1,4,19,20,21,22,23], laser-plasma interaction [7,24], and Bose-Einstein condensates [25,26,27,28]. Another important reason for the interest in the CQNLSE is that due to its nonintegrability it allows one to observe dynamical effects that do not exist in the CNLSE, e.g., emission of continuous radiation in twosoliton collisions [29,30].…”

“…4in the vicinity of pm. The dashed line corresponds to the asymptotic loglognormal PDF given by Eq (24)…”

Stochastic perturbation of solitons for Alfven waves in plasmas

“…Eq. (1) has infinitely many conserved quantities [1,12,13]. However, the first three of those conserved quantities are…”

Solitons in Plasmas: A Lie Symmetry Approach

“…The nonlinear Schröinger's equation (NLSE) in its dimensionless form has important applications in Plasma Physics [1][2][3][4][5][6][7][8][9][10]. It describes the electron (Langmuir) waves [2,9].…”