非线性电报方程行波解的定性分析与求解  

Qualitative analysis and traveling wave solutions of nonlinear telegraph equation

作　　者：李想[1] 张卫国[1] 赵岩[2] 

机构地区：[1]上海理工大学理学院,上海200093 [2]南京信息工程大学数理学院,南京210044

出　　处：《上海理工大学学报》2011年第4期372-378,共7页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11071164);上海市重点学科建设资助项目(S30501);上海市自然科学基金资助项目(10ZR1420800)

摘　　要：利用平面动力系统的理论和方法研究了非线性电报方程的有界行波解.分析结果表明,非线性电报方程有且仅有两个有界行波解,并且当耗散作用较大时非线性电报方程的有界行波解呈扭状孤波解形式,而当耗散作用较小时呈衰减振荡解形式.在此基础上,利用假设待定法求出了对应耗散作用较大时方程的一种扭状孤波解的精确解,以及对应耗散作用较小时方程的衰减振荡解近似解.进一步运用齐次化原理,建立反映衰减振荡解精确解和近似解关系的积分方程,得到了衰减振荡近似解的误差估计.Bounded traveling wave solutions of nonlinear telegraph equation were discussed by use of the theory and method of planar dynamical systems. The results indicate that the nonlinear tele- graph equation has only two bounded traveling wave solutions. When the dissipation effect is strong, the bounded traveling wave solutions of nonlinear telegraph equation appear as kink solitary wave solutions; and when it is weak, they appear as damped oscillatory solutions. Based on the above discussion, a kink solitary wave solution corresponding to the strong dissipation effect, and approximate damped oscillatory solutions corresponding to the weak dissipation effect were obtained by using undetermined coefficients method. Furthermore, base on homogenization principle, the error estimates of approximate damped oscillatory solutions were given by establishing the integral equations reflecting the relations between exact solutions and approximate solutions.

关 键 词：非线性电报方程 平面动力系统 衰减振荡解 近似解 误差估计 

分 类 号：O175.2[理学—数学]