长短波演化方程的孤波解、周期波解及它们之间的演变关系  

Periodic Wave Solutions and Solitary Wave Solutions of Long-Short Wave Evolution Equation and Evolution Relationship Between Both Solutions

作　　者：时慧芳 张卫国[1] SHI Huifang;ZHANG Weiguo(College of Science,University of Shanghai for Science and Technology,Shanghai 200093, China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《应用数学》2019年第1期222-233,共12页Mathematica Applicata

基　　金：国家自然科学基金(11471215)

摘　　要：本文运用定性分析与首次积分相结合的方法研究了长短波演化方程的精确孤波解、周期波解以及这两种解之间的演变关系.揭示出所研方程之所以会出现周期波解和孤波解,本质上是由该方程解中短波u的模对应的Hamilton系统的能量取不同的值所决定的.In this paper, we focus on studying the exact solitary wave solutions and periodic wave solutions of long-short wave evolution equation, as well as the evolution relationship between these solutions by combining qualitative analysis with first integration. It is concluded that the essential reason of periodic wave solutions and solitary wave solutions is the different values for the energy of Hamiltonian system corresponding to this equation.

关 键 词：动力系统理论 孤波解 周期波解 演变关系 

分 类 号：O175.21[理学—数学]