Degasperis-Procesi方程的类孤子新解  

New Soliton-like Solutions of Degasperis-Procesi Equation

作　　者：伊丽娜[1] 包俊东[1] 套格图桑[1] 

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《数学的实践与认识》2017年第4期187-193,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502);内蒙古师范大学研究生科研创新基金项目(CXJJS16081)资助的课题

摘　　要：利用辅助方程与函数变换相结合的方法,构造了Degasperis-Procesi(D-P)方程的无穷序列类孤子新解.首先,通过两种函数变换,把D-P方程化为常微分方程组.然后,利用常微分方程组的首次积分,把D-P方程的求解问题化为几种常微分方程的求解问题.最后,利用几种常微分方程的Bcklund变换等相关结论,构造了D-P方程的无穷序列类孤子新解.这里包括由Riemannθ函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数组成的无穷序列光滑孤立子解、尖峰孤立子解和紧孤立子解.The method for combing the auxiliary equation with the function transformations is presented to search for new infinite sequence soliton-like solutions of Degasperis-Procesi（D- P） equation. Firstly, two function transformations are applied to change D-P equation into a set of ordinary differential equations. Then the problem of solving the solutions of D-P equation is transformed into the problem of solving the solutions of several normal ordinary differential equations according to the first integral of the set of the ordinary differential equa- tions. Finally, new infinite sequence soliton-like solutions of D-P equation are constructed by using B^icklund transformation of the several ordinary differential equations and other relative conclusions. The solutions include infinite sequence smooth soliton solutions, peak soliton solutions and compact soliton solutions composed of Riemann ~ function, Jacobi elliptic function, hyperbolic function, trigonometric function and rational function.

关 键 词：函数变换 DEGASPERIS-PROCESI方程 Bcklund变换 无穷序列类孤子新解 

分 类 号：O175.29[理学—数学]