State transition of lump-type waves for the (2+1)-dimensional generalized KdV equation
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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.
Keywords(2+1)-Dimensional generalized Korteweg–de Vries equation Hirota bilinear method Lump-type wave State transition
The authors would like to express their sincere thanks to the referees for their enthusiastic guidance and help. This work is supported by the National Natural Science Foundation of China (No. 11801240) and the Fund for Fostering Talents in Kunming University of Science and Technology (No. KKSY201707021).
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Conflicts of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.