N -Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively. (paper)