Auto-Bäcklund transformation and exact solutions for modified nonlinear dispersive mK(m,n) equations

Based on the idea of homogenous balance method and with the help of Mathematica, we obtain a new auto-Bäcklund transformation for modified nonlinear dispersive equation mK(m,n). Then based on the Bäcklund transformation, some solitary patterns solution for mK(m,n) equation are derived. In addition, we also obtain the general solutions for mK(n,n) in higher dimensional spatial domains, even in N dimensional space.