一类扰动复Swift-Hohenberg方程的精确孤立子解  

Exact Soliton Solutions for the Dimensional Complex Quintic Swift-Hohenberg Equation with a Dissipative Term

作　　者：龙林园 杨立新[2] 徐衍聪[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036 [2]浙江同济科技职业学院数理学院,浙江杭州311231

出　　处：《杭州师范大学学报（自然科学版）》2015年第6期625-631,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY13A010020);杭州师范大学科研基金项目(HNUEYT2013)

摘　　要：利用Painlevé分析、Hirota多元线性法和直接拟设技巧,研究了一维带有耗散项的五次复SwiftHohenberg方程的解析解.找到了方程的精确解并证明方程系数之间存在着某种关系.得到了包括特殊类型的孤波解、暗孤子解和以雅可比椭圆函数形式表示的周期解等,为光学的进一步研究提供了一系列孤子解.Analytic solutions for the dimensional quintic complex Swift-Hohenberg equation with a dissipative term are investigated by using Painlevéanalysis,the Hirota multi-linear method and a direct ansatz technique.This paer finds exact solutions exist to the equation and proves that there is certain relation among the coefficients.The set of solutions consist of particular types of solitary wave solutions,dark soliton solutions and periodic solutions in terms of elliptic Jacobi functions are obtainde.In fact,these muliti-parameter families of solutions can act as a seeding set of solutions which can be very useful in optical studies.

关 键 词：孤立子 PAINLEVÉ分析 Hirota多元线性法 SWIFT-HOHENBERG方程 直接拟设法 

分 类 号：O175.4[理学—数学]