This article is cited in 1 paper

Dynamics of the generalized $(3+1)$-dimensional nonlinear Schrödinger equation in cosmic plasmas

Hui-Ling Zhen^ab, Bo Tian^ab, Min Li^ab, Yan Jiang^ab, Ming Wang<sup>ab

a</sup> School of Science, P.O.Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
^b State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract: Under investigation in this paper is a generalized $(3+1)$-dimensional nonlinear Schrödinger equation with the variable coefficients, which governs the nonlinear dynamics of the ion-acoustic envelope solitons in the magnetized electron-positron-ion plasma with two-electron temperatures in space or astrophysics. Bilinear forms and Bäcklund transformations are derived through the Bell polynomials. $N$-soliton solutions are constructed in the form of the double Wronskian determinant and the $N$-th order polynomials in $N$ exponentials. Shape and motion of one soliton have been graphically analyzed, as well as the interactions of two and three solitons. When $\beta(t)$ and $\gamma(t)$ are both the periodic functions of the reduced time $t$, where $\gamma(t)$ is the loss (gain) coefficient, and $\beta(t)$ means the combined effects of the transverse perturbation and magnetic field, the shape and motion of one soliton as well as the interactions of two or three solitons will occur periodically. All the interactions can be elastic with certain coefficients.

Key words: generalized $(3+1)$-dimensional nonlinear Schrödinger equation, double Wronskian determinant, $N$-soliton solutions, Bäcklund transformation, Bell polynomials.

UDC: 519.634

Received: 24.05.2013
Revised: 20.07.2013

Language: English

DOI: 10.7868/S0044466914030089

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:3, 512–521

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