拉普拉斯变换法求解超短脉冲方程  

Solving the Ultra-short Pulse Equation by the Laplace Transform Method

作　　者：张景军[1] 郭艳凤[2] ZHANG Jing-jun;QUO Yan-feng(College of Mathematics,Physics and Information Engineering,Jinxing University,Jinxing 314001,China;College of Science,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]嘉兴学院数理与信息工程学院,浙江嘉兴314001 [2]广西科技大学理学院,广西柳州545006

出　　处：《数学的实践与认识》2018年第21期220-225,共6页Mathematics in Practice and Theory

基　　金：广西高等教育本科教学改革工程项目(2016JGB274);广西科技大学优秀教学团队建设项目;浙江省自然科学基金项目(LY17A010025);广西自然科学基金(2017GXNSFAA198221)

摘　　要：讨论一类超短脉冲方程,它描述超短脉冲在光纤中的传播现象,利用拉普拉斯变化法,证明了方程初边值问题古典解的存在唯一性,同时也分析了基函数的渐近性质.讨论内容既可为偏微分方程课程教学提供素材,同时也为其非线性方程的进一步研究奠定基础.This paper deals with a kind of ultra-short pulse equation, which describes the propagation of ultra-short pulses in optical fibers. By using the Laplace transform method,we prove the existence and uniqueness of the initial-boundary value problem for this equation.Also, we discuss the asymptotic behavior for the kernel function. The contents of the paper not only provide rich materials in teaching for the course of partial differential equations, but also establish a good foundation in the further research for the nonlinear form of the ultra-short pulse equation.

关 键 词：拉普拉斯变换 超短脉冲方程 古典解 渐近性 

分 类 号：O175[理学—数学]