| Citation: |
Wen-Xiu Ma. A SEARCH FOR LUMP SOLUTIONS TO A COMBINED FOURTH-ORDER NONLINEAR PDE IN (2+1)-DIMENSIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1319-1332. doi: 10.11948/2156-907X.20180227
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A SEARCH FOR LUMP SOLUTIONS TO A COMBINED FOURTH-ORDER NONLINEAR PDE IN (2+1)-DIMENSIONS
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Abstract
We aim to explore new (2+1)-dimensional nonlinear equations which possess lump solutions. Through the Hirota bilinear method, we formulate a combined fourth-order nonlinear equation while guaranteeing the existence of lump solutions. The class of lump solutions is constructed explicitly in terms of the coefficients of the combined nonlinear equation via symbolic computations. Specific examples are discussed to show the richness of the considered combined nonlinear equation. Three dimensional plots and contour plots of specific lump solutions to two specially chosen cases of the equation are made to shed light on the presented lump solutions.-
Keywords:
- Lump solution /
- Hirota bilinear method /
- integrable equation /
- symbolic computation /
- soliton
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References
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Wen-Xiu Ma. A SEARCH FOR LUMP SOLUTIONS TO A COMBINED FOURTH-ORDER NONLINEAR PDE IN (2+1)-DIMENSIONS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1319-1332. doi: 10.11948/2156-907X.20180227
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Figure 1. Profiles of
$ u_1 $ when$ t = 0, 15, 30 $ : 3d plots (top) and contour plots (bottom) -
Figure 2. Profiles of
$ u_2 $ when$ t = 0, 50, 100 $ : 3d plots (top) and contour plots (bottom)