一类复合的修正BBM方程的精确行波解

The Exact Traveling Wave Solutions for a Class of Composite Modified BBM Equations

研究一类复合的修正BBM方程,其是对修正BBM方程的改进。探讨该方程在非线性项同时含有u_(xxt)项和u_(xxx)项时解的结构变化。通过引入行波变换,将该方程转化为常微分方程组。基于首次积分法,获得复合的修正BBM方程若干行波解的精确表达式,并利用Maple绘制其特解图形。结果表明,复合的修正BBM方程不仅有新的周期行波解,而且有新的非周期行波解。

In this paper,a class of composite modified BBM equations is studied,which is an improvement of the modified BBM equations.The structural change of the solution of the equation is discussed where the nonlinear terms contain u_(xxt) and u_(xxx).By introducing the traveling wave transform,the differential equation is transformed into an ordinary differential system.Based on the first integral method,the exact expressions of several traveling wave solutions of the compound modified BBM equation are obtained,and its graphs of particular solutions are drawn by using Maple.The results show that the modified BBM equation have not on⁃ly new periodic traveling wave solutions,but also new aperiodic traveling wave solutions.