| Summary: | The main purpose of this paper is to learn N-soliton, M-lump, breather solutions and interaction solutions for a KdV equation with variable coeffificients. Using the Hirota bilinear method, one-soliton, two-soliton, three-soliton and N-soliton are obtained. By taking the conjugate parameters for two-soliton amd four-soliton, one-breather and two-breather waves are obtained, respectively. The long wave limit technique is applied to two-soliton, four-soliton and six-soliton, one-lump, two-lump and three-lump solutions are obtained, respectively. Furthermore, the interaction solutions are constructed, including one-breather and one-soliton, one-breather and two-soliton, one-lump and one-soliton, one-lump and two-soliton. In order to discussing the dynamical properties of the above solutions, some 3D-plots, 2D-plots, contour plots and density plots of these solutions are given.
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