Mixed lump-kink solutions to the KP equation

Abstract

By using the Hirota bilinear form of the KP equation, twelve classes of lump-kink solutions are presented under the help of symbolic computations with Maple. Analyticity is naturally achieved by taking special choices of the involved parameters to guarantee a positive constant term. A key step in generating lump-kink solutions is to combine quadratic functions and the exponential function in the second-order logarithmic derivative transformation.