非线性Schrdinger方程的Compacton解和孤立波解

Compacton and solitary solutions for nonlinear Schrdinger equation

研究了非线性Schro..dinger方程:iut+αuxx+β|u|2pu=0(p为任意实数),得到丰富的孤立波解:当p>0时得到孤立波解,p<0时得到移动Compacton解,p=0时得到Compacton解;研究了(2+1)维非线性Schro..dinger方程的解,并推广到(n+1)维非线性Schro..dinger方程 还比较了任意维非线性Schro..

Nonlinear Schro..dinger equation such as iu_t+αu_(xx)+β|u|^(2p)u=0 is studied and abundant solutions is obtained: when p>0, solitary solutions; when p<0, envelope displacement compactons; when p=0, compacton solutions. (2+1) dimension nonlinear Schro..dinger equation and (n+1) dimension nonlinear Schro..dinger equation are also studied. The solutions are compared in arbitrary dimensions as well as the relationship between different solutions and parameters.