| Citation: |
Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng, Lu-Lu Geng. CHARACTERISTICS OF NEW TYPE ROGUE WAVES AND SOLITARY WAVES TO THE EXTENDED (3+1)-DIMENSIONAL JIMBO-MIWA EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2722-2735. doi: 10.11948/20200402
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CHARACTERISTICS OF NEW TYPE ROGUE WAVES AND SOLITARY WAVES TO THE EXTENDED (3+1)-DIMENSIONAL JIMBO-MIWA EQUATION
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Abstract
On the basis of the binary Bell polynomial scheme, the bilinear form of the extended (3+1)-dimensional Jimbo-Miwa (JM) equation, is constructed. Then, a class of new type rogue waves solutions to the extended (3+1)-dimensional JM equation, is found. It mainly includes the lump solutions, lumpoff solutions and instanton solutions. Their nonlinear evolutionary processes by 3D- and 2D-graphs, are shown. Finally, a direct method which is called the tanh-function method was used to get solitary waves of this considered model. These results can help us better understand interesting physical phenomena and mechanism.
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Keywords:
- Extended (3+1)-dimensional JM equation /
- bilinear form /
- rogue waves /
- solitary waves
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References
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Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng, Lu-Lu Geng. CHARACTERISTICS OF NEW TYPE ROGUE WAVES AND SOLITARY WAVES TO THE EXTENDED (3+1)-DIMENSIONAL JIMBO-MIWA EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2722-2735. doi: 10.11948/20200402
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Figure 1. Plots of the lump solution
$ {u_{case_{2}}} $ with parameters$ {a_1} = 1, {k_2} = -2, {k_4} = 1 $ . (a) 3D-plot, with$ z = 20 $ . (b) 2D-contour plot. -
Figure 2. Plots of evolution of the lumpoff structures of solution
$ {u_{case_{5}}} $ with parameters$ {a_4} = 1, {k_2} = -2, {k_4} = 1, {k_5} = {a_5} = 0, b = -10, z = 2 $ . (a)$ t = -20 $ . (b)$ t = 0 $ . (c)$ t = 20 $ . -
Figure 3. Plots of the instanton structures of solution
$ {u_{case_{15}}} $ with parameters$ {a_4} = 1, {k_2} = -2, {k_4} = 1, {k_5} = {a_5} = 0, b = -10, z = t = 0 $ . (a) 3D-plot,$ a = 2, b = -2 $ . (b) 3D-plot,$ a = -2, b = 2 $ .(c) 3D-plot,$ a = 2, b = -1 $ .