一类充分非线性方程Compacton解和孤立波解

Compacton and solitary solutions for one type of fully nonlinear equation

研究一类五阶充分非线性色散方程:um-1ut±a(un)x+b(uk)xxx+c(uq)xxxxx=0(nkq≠0), 用拟设法求出它的Compacton解和周期波解及其孤立波解,讨论不同非线性参数情况下解的变化.另外研究了(2+1)维和(3+1)维充分非线性色散方程的解,并推广到(n+1)维充分非线性色散方程.

One type of five-order fully nonlinear dispersive equations such as u^(m-1)u_t±a(u^n)_x+(b(u^k)_(xxx)+)c(u^q)_(xxxxx)=0(nkq≠0) are studied and compacton solutions, periodic wave solutions and solitary solutions are obtained by using ansatzs method. The changes of Compacton solutions with various nonlinear parameters are discussed. (2+1) dimension, (3+1) dimension and (n+1) dimension fully nonlinear dispersive equations are also studied.