一类非线性演化方程的新精确周期解

New exact periodic solutions to a category of nonlinear evolution equations

在原Jacobi椭圆函数展开法的基础上,又引进了其余几种Jacobi椭圆函数Glaisher符号,扩展了Liu等提出的Jacobi椭圆函数展开法,并以mBBM方程和Gardner方程为例,借助数学软件———Mathematica,求得了它们的一系列精确周期解,这些解在极限条件下可退化为孤立波解和三角函数解.

Based on the original expansion method of Jacobi elliptic function, other Jacobi elliptic funetions--Glaisher symbol are introduced and expansion method of Jacobi elliptic function presented by Liu is expanded. Taking the mBBM equation and Gardner equation as examples, a series of new exact periodic solutions are obtained for these equations is found with the help of mathematics software--Mathematica. These solutions can degenerate into solitary wave solutions or trigonometric function solutions under a critical condition.