Abstract
In this paper, we are mainly concerned with the (2+1)-dimensional generalized Korteweg–de Vries equation in fluid dynamics. Based on the translation transformation and Hirota bilinear method, we study the excitations of nonlinear lump-type waves on a constant background. A remarkable feature of these lump-type waves is that under some parameter conditions, these lump-type wave solutions can be converted into some amusing nonlinear wave structures, including the W-shaped solitary wave, double-peak solitary wave, parallel solitary wave, multi-peak solitary wave and periodic wave solutions. These results do not have an analog in the standard Kadomtsev–Petviashvili equation. The transition condition between the lump-type wave and other nonlinear wave solutions is presented. The dynamical behaviors of these nonlinear wave solutions are investigated analytically and illustrated graphically. Furthermore, the existence conditions for these nonlinear wave solutions are exhibited explicitly. Our results further enrich the nonlinear wave theories for the (2+1)-dimensional generalized Korteweg–de Vries equation.
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