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Degasperis-Procesi方程的类孤子新解
引用本文:伊丽娜,包俊东,套格图桑. Degasperis-Procesi方程的类孤子新解[J]. 数学的实践与认识, 2017, 0(4): 187-193
作者姓名:伊丽娜  包俊东  套格图桑
作者单位:内蒙古师范大学数学科学学院,内蒙古呼和浩特,010022
基金项目: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.

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

New Soliton-like Solutions of Degasperis-Procesi Equation
YI Li-na,BAO Jun-dong,Taogetusang. New Soliton-like Solutions of Degasperis-Procesi Equation[J]. Mathematics in Practice and Theory, 2017, 0(4): 187-193
Authors:YI Li-na  BAO Jun-dong  Taogetusang
Abstract: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 equations.Finally,new infinite sequence soliton-like solutions of D-P equation are constructed by using Backlund 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 θ function,Jacobi elliptic function,hyperbolic function,trigonometric function and rational function.
Keywords:function transformation  Degasperis-Procesi equation  B(a)cklund transformation  new infinite sequence soliton-like solutions
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