Bäcklund transformation, non-local symmetry and exact solutions for \((2+1)\)-dimensional variable coefficient generalized KP equations (Q1570385)

The author deals with \((2+1)\)-dimensional variable coefficient KP equations which is the integrable model \[ G(u)\equiv u_{xt}+ h_1 (u_{xxx}+ 6uu_x+ 6h_3 u_x)_x+ h_2 u_{yy}- (h_3+ 12 h_1 h_3^2)= 0, \] where \(h_1= h_1(t)\), \(h_2= h_2(t)\) and \(h_3= h_3(t)\) are arbitrary functions of \(t\). Recently, improving the homogeneous balance method the author applied it to KdV, KP, variable coefficient KdV and \((2+1)\)-dimensional KPP equations. Here the author extends the method to \((2+1)\)-dimensional variable coefficient generalized KP equations. As a result, a Bäcklund transformation and a nonlocal symmetry are found. Then by using the Bäcklund transformation, six families of exact solutions for \((2+1)\)-dimensional variable coefficient KP equations are obtained, which contain new soliton-like solutions.