一类非线性强度Boussinesq方程的Compacton解和孤立波解

Compacton solution and solitary wave solution for a class of nonlinear intensity Boussinesq equation

研究一类非线性强度的Boussinesq方程:um-1utt-uxx-a(un)xx+b(uk)xxxx=0,用拟设法求出方程的Compacton解(即在有限区间外为0的孤立波解)和周期解以及孤立波解,讨论维数参数满足m=n=k,m=k≠n和m=n≠k下解的结构,并作出它们的图像.另外研究了(2+1)维和(3+1)维方程的解,并推广到(n+1)维方程的解.

A kind of nonlinear Boussinesq equation, u^m-1utt-uxx-a（u^n）xx ＋ b （u^k）xxxx=0, is studied. By the analogic method, the Compacton solution（ the solitary wave solution is zero out of finite range）, solitary wave solution and periodic wave solution are obtained under the condition when m = n = k, m = k ≠ n and m = n ≠ k. Their figs are drawn. Furthermore, the solution for （ 2 ＋ 1 ） dimension and （3 ＋ 1 ） dimension, and extending to （ n ＋ 1 ） dimension as well are also studied.