新型广义KdV方程K(m,n,1)的Compacton解

Compacton Solutions of New Generalized KdV Equation K(m,n,1)

研究了一类新型的广义KdV方程K(m,n,1):ut+β1(um)x+β2(un)3x+β3u5x=0(m,n>1),用拟设法求出了它的Compacton解(即在有限区间外为0的孤波解),得到它的图像 并且考虑了Hamiton结构和守恒量,得到了三个守恒量 最后推广到一般的形式ut+β1(uk)x+ nβi(uk)(2i-1)x+βn+1u(2n+1)x=0

A new generalized KdV equation K(m,n,1) is studied,namely ut+β1(um)x+β2(un)3x+β3u5x=0(m,n>1). By the analogic method, the Compacton solution (the solitary wave solution is zero out of finite range) is obtained, its figs are drawn. Consider its Hamitonian and conservations, three conservation solutions are obtained. At last its generalized equation ut+β1(uk)x+ni=1βi(uk)(2i-1)x+βn+1u(2n+1)x=0 is studied.