一类非线性色散方程中的新型奇异孤立波

New exotic solitary waves in one type of nonlinear dispersive equations

研究一类非线性色散广义DGH方程的新型奇异孤立波及其Painlev啨可积性.利用Painlev啨分析发现当对流项强度m=2时广义DGH方程是可积的,这是一个新的可积方程.通过构造新的变量代换以及auto-Backlund变换获得该方程丰富的奇异孤立波解,如紧孤立波(compacton)、尖峰孤立波(peakon)、新型带尖点的双孤立波和带爆破点的双孤立波等.

New exotic solitary wave and the painleve integrability of one type of the nonlinear dispersive generalized DGH equation are studied. By Painleve analysis, we discover that the nonlinear dispersive generalized DGH equation with m = 2 is integrable, which is a new integrable equation. By the new variable transformation and the auto-Backlund transformation, we obtain abundant exotic solitary wave solutions, such as eompactons, peakons, new double solitary waves with peak points, and double solitary waves with blow-up points.