Symbolic computation on Bäcklund transformation and soliton solutions for a generalized nonlinear Schrödingere quation in the inhomogeneous fibers
首发时间:2012-02-07
Abstract:Under investigation in this paper is a generalizednonlinear Schrödinger (NLS) equation with the variable dispersion,electro-optic phase modulation and fiber gain/loss coefficients,which governs the propagation of solitons in an inhomogeneous fibermedium. Via the Hirota method and symbolic computation, one-, two-,N-soliton solutions and bilinear Bäcklund transformation areobtained. Condition assuring the solutions without singularities hasbeen given. Propagation and interaction of solitons have beendiscussed analytically and graphically with respect to such physicalquantities as the amplitudes, velocities and widths. Via theasymptotic analysis, it is found that the interaction between thetwo solitons is elastic.
keywords: Partial differential equation Bäcklund transformation Soliton solutions Hirotamethod Symbolic computation
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非均匀光纤中扩展的非线性薛定谔方程的Backlund变换和孤子解
摘要:本文将研究一个变系数的扩展的非线性薛定谔方程,该方程用于描述非均匀光纤介质中孤子的传播。通过双线性方法和计算机符号计算,得到了该方程的单孤子,双孤子和N孤子解,以及Backlund变换。同时给出了解中不出现奇点的条件。孤子的传播和相互作用性质分别从振幅,速度和宽度等方面进行了解析和图示分析。最后,通过渐近分析,得到了双孤子之间的碰撞是弹性的。
关键词: 偏微分方程 Backlund变换 孤子解 双线性方法 计算机符号计算
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