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

作　　者：吴双军[1] 田立新[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第B12期5-9,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(100710331);江苏省自然科学基金资助项目(BK2002003)

摘　　要：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.

关 键 词：COMPACTON解 多重Compacton解 孤立波解 周期波解 

分 类 号：O193[理学—数学]