一维非线性传输线方程的精确解

journal6 ›› 2003, Vol. 24 ›› Issue (3): 23-26.

一维非线性传输线方程的精确解

(西北师范大学物理与电子工程学院,甘肃兰州730070)

出版日期:2003-09-15 发布日期:2012-11-07
作者简介:石玉仁(1975-)，男，甘肃省金昌市人，硕士，西北师范大学物理与电子工程学院讲师，主要从事计算物理研究.
基金资助:
国家自然科学基金资助项目(10247008)

Exact Solutions of One-Dimensional Nonlinear Transmission Line Equation

(College of Physics and Electronic Engineering,Northwest Normal University,Lanzhou 730070,Gansu China)

Online:2003-09-15 Published:2012-11-07

摘要/Abstract

摘要：利用齐次平衡法得到一维非线性传输线方程的Backlund变换和它的孤立子解，然后对此孤立子解的稳定性进行分析.结果表明，在Lyapunov线性稳定性意义下,该解是条件稳定的，说明在非线性传输线中可以存在稳定传播的孤立子.同时，对齐次平衡法的思想进行了扩展,并在此基础上得到非线性传输线方程的另1组孤立子解和1组具有奇异性的孤立波解.

关键词： 非线性传输线方程, 齐次平衡法, 孤子解

Abstract: The author derived the Backlund transformation and a soliton solution of one-dimensional nonlinear transmission line equation by using the homogeneous balance method.Theoretical analysis to the stability of this solution was done.The result indicates that the soliton solution is conditional stability at the meaning of Lyapunov linear stability.It shows that stable soliton can be existed in nonlinear transmission line.Based on the extended thought of the homogeneous balance method,another soliton solution and a solitary wave solution of the nonlinear transmission line equation were obtained.

Key words: nonlinear transmission line equation, homogeneous balance method, soliton solution

石玉仁, 段文山, 吕克璞, 杨红娟. 一维非线性传输线方程的精确解[J]. journal6, 2003, 24(3): 23-26.

SHI Yu-Ren, DUAN Wen-Shan, 吕Ke-Pu , YANG Hong-Juan. Exact Solutions of One-Dimensional Nonlinear Transmission Line Equation[J]. journal6, 2003, 24(3): 23-26.