Bäcklund Transformations and Solutions of Some Generalized Nonlinear Evolution Equations

Using the method of separation of variables based on Bäcklund transformation, new classification results with exact solutions for various generalized nonlinear evolution equations such as the KdV-type equations, the NNV-type equations and the Schrödinger-type equations are obtained. We also present a unified construction method for nonlinear evolution equations which admit separation of variable and the main tool is a class of generalized multidimensional binary Bell polynomials.