| Citation: |
Huiling Wu, Hongyu Wu, Quanyong Zhu, Jinxi Fei, Zhengyi Ma. SOLITON, BREATHER AND LUMP MOLECULES IN THE (2+1)-DIMENSIONAL B-TYPE KADOMTSEV-PETVIASHVILI-KORTEWEG DE-VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 230-244. doi: 10.11948/20210132
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SOLITON, BREATHER AND LUMP MOLECULES IN THE (2+1)-DIMENSIONAL B-TYPE KADOMTSEV-PETVIASHVILI-KORTEWEG DE-VRIES EQUATION
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Abstract
The $ N $-soliton solutions of the (2+1)-dimensional B-type Kadomtsev-Petviashvili-Korteweg de-Vries (BKP-KdV) equation are constructed through the Hirota bilinear method. By inserting the velocity resonance conditions into the soliton solutions, soliton molecule, breather molecule, breather-soliton molecule, lump-soliton molecule and lump-breather molecule are presented. The interaction of two soliton molecules, and the interaction between one soliton molecule and breather are discussed and shown to be the elastic collisions.
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References
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Huiling Wu, Hongyu Wu, Quanyong Zhu, Jinxi Fei, Zhengyi Ma. SOLITON, BREATHER AND LUMP MOLECULES IN THE (2+1)-DIMENSIONAL B-TYPE KADOMTSEV-PETVIASHVILI-KORTEWEG DE-VRIES EQUATION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 230-244. doi: 10.11948/20210132
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Figure 1. (a) The soliton molecule with the parameters (2.12), (2.13) and (2.14) at
$ t = 0 $ . (b) The breather with the parameters (2.16), (2.9) and (2.20) at$ t = 0 $ . (c) The lump structure given by (2.29) at$ t = 0 $ . (d)-(f) are the corresponding density figures (a)-(c), respectively. -
Figure 2. Interaction of one soliton molecule and a line soliton for the (2+1)-dimensional BKP-KdV equation (1.3) with the parameters (2.33) and (2.34) at (a)
$ t = -5 $ , (b)$ t = 0 $ and (c)$ t = 5 $ , respectively. -
Figure 3. The soliton-breather molecule for the (2+1)-dimensional BKP-KdV equation (1.3) with the parameters (2.36) and (2.37) at (a)
$ t = -2 $ , (b)$ t = 0 $ and (c)$ t = 2 $ , respectively. -
Figure 4. The soliton-lump molecule in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameters (2.28) and (2.41) at (a)
$ t = -1.2 $ , (b)$ t = 0 $ and (c)$ t = 1.2 $ , respectively. -
Figure 5. The elastic interaction between two soliton molecules in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameters (2.43) at (a)
$ t = -2 $ , (b)$ t = 0 $ and (c)$ t = 2 $ , respectively. -
Figure 6. The molecule consisting of one soliton molecule and one breather in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameter (2.44) and (2.45) at (a)
$ t = -16 $ , (b)$ t = 0 $ and (c)$ t = 16 $ , respectively. -
Figure 7. The elastic interaction between one soliton molecule and one breather in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameter (2.44) and (2.45), but
$ \kappa = -\frac{2}{5},\;{\eta _2} = 5,\ \ \rho = \frac{{1}}{{5}},\;\varrho = \frac{{2}}{{5}} $ at (a)$ t = -16 $ , (b)$ t = 0 $ and (c)$ t = 16 $ , respectively. -
Figure 8. The molecule consisting of one breather and one lump in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameter (2.46), (2.47) and (2.48) at (a)
$ t = -\frac{1}{2} $ , (b)$ t = 0 $ and (c)$ t = \frac{1}{2} $ , respectively. -
Figure 9. The elastic interaction between one breather and one lump in the (2+1)-dimensional BKP-KdV equation (1.3) with the parameters (2.20) and (2.28) at (a)
$ t = -2 $ , (b)$ t = 0 $ and (c)$ t = 2 $ , respectively.