| Volume 10, Number 3, 2020, Pages 935-945 DOI：10.11948/20190162 |
| Lumps and their interaction solutions of a (2+1)-dimensional generalized potential Kadomtsev-Petviashvili equation |
| Bo Ren,Ji Lin,Zhi-Mei Lou |
| Keywords:Generalized potential Kadomtsev-Petviashvili equation, Hirota bilinear form, lump wave, lump-soliton. |
| Abstract: |
| A (2+1)-dimensional generalized potential Kadomtsev-Petviashvili (gpKP) equation which possesses a Hirota bilinear form is constructed. The lump waves are derived by using a positive quadratic function solution. By combining an exponential function with a quadratic function, an interaction solution between a lump and a one-kink soliton is obtained. Furthermore, an interaction solution between a lump and a two-kink soliton is presented by mixing two exponential functions with a quadratic function. This type of lump wave just appears to a line $k_2x+k_3y+k_4t+k_5 \sim 0$. We call this kind of lump wave is a special rogue wave. Some visual figures are depicted to explain the propagation phenomena of these interaction solutions. |
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