摘要
研究了Lie对称、守恒律、约化和Benjamin-Bona-Mahony(BBM)方程的精确解.运用乘子方法可以得到BBM方程的三个守恒律,根据这个方法我们发现守恒向量的Lie对称有两种不同形式.运用广义双约化理论将三阶BBM方程约化成二阶常微分方程,运用Sine-Cosine方法求出约化后的常微分方程的新的精确解.
We study the Lie symmetries,conservation laws,reductions,and new exact solutions of Benjamin-Bona-Mahony(BBM).The multiplier approach gets three conservation laws for BBM equation.We find the Lie symmetries is associated with the conserved vectors,and has two different cases arise.In this paper,the generalized double reduction theorem is then applied to reduce the third-order BBM equation to a second-order ordinary differential equation(ODE)and the implicit solutions are established.We use the Sine-Cosine method for the reduced second-order ODE to obtain the new explicit solutions of BBM equation.
作者
姜文涛
石剑平
JIANG Wentao;SHI Jianping(School of Sciehce,Kunming University of Science and Technology,Kunming 650500,China)
出处
《河南科学》
2019年第1期1-9,共9页
Henan Science
基金
国家自然科学基金(11261025
11026309)
关键词
LIE对称
守恒律
双约化
精确解
Lie symmetries
conservation laws
double reduction theory
exact solutions
