Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics
In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/8249635 |
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| author | Zhonglong Zhao Lingchao He Yubin Gao |
| author_facet | Zhonglong Zhao Lingchao He Yubin Gao |
| author_sort | Zhonglong Zhao |
| collection | DOAJ |
| description | In this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8-lump solutions are presented, respectively. The 3-lump wave has a “triangular” structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation. |
| format | Article |
| id | doaj-art-d08a46dfe83d49cb8bc9909e09a87ed7 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-d08a46dfe83d49cb8bc9909e09a87ed72025-02-03T05:59:29ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/82496358249635Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid MechanicsZhonglong Zhao0Lingchao He1Yubin Gao2Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaIn this paper, the bilinear method is employed to investigate the rogue wave solutions and the rogue type multiple lump wave solutions of the (2+1)-dimensional Benjamin-Ono equation. Two theorems for constructing rogue wave solutions are proposed with the aid of a variable transformation. Four kinds of rogue wave solutions are obtained by means of Theorem 1. In Theorem 2, three polynomial functions are used to derive multiple lump wave solutions. The 3-lump solutions, 6-lump solutions, and 8-lump solutions are presented, respectively. The 3-lump wave has a “triangular” structure. The centers of the 6-lump wave form a pentagram around a single lump wave. The 8-lump wave consists of a set of seven first order rogue waves and one second order rogue wave as the center. The multiple lump wave develops into low order rogue wave as parameters decline to zero. The method presented in this paper provides a uniform method for investigating high order rational solutions. All the results are useful in explaining high dimensional dynamical phenomena of the (2+1)-dimensional Benjamin-Ono equation.http://dx.doi.org/10.1155/2019/8249635 |
| spellingShingle | Zhonglong Zhao Lingchao He Yubin Gao Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics Complexity |
| title | Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics |
| title_full | Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics |
| title_fullStr | Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics |
| title_full_unstemmed | Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics |
| title_short | Rogue Wave and Multiple Lump Solutions of the (2+1)-Dimensional Benjamin-Ono Equation in Fluid Mechanics |
| title_sort | rogue wave and multiple lump solutions of the 2 1 dimensional benjamin ono equation in fluid mechanics |
| url | http://dx.doi.org/10.1155/2019/8249635 |
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