Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg–de Vries equation in a fluid

Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg–de Vries equation in a fluid

Fluids are studied in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a (3+1)-dimensional Korteweg–de Vries equation in a fluid. Bilinear form and N -soliton solutions are obtained, where N is a positive integer. Via the N -soliton solutions, we...

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Bibliographic Details
Published in:Nonlinear dynamics 2021-08, Vol.105 (3), p.2525-2538
Main Authors: Cheng, Chong-Dong, Tian, Bo, Zhang, Chen-Rong, Zhao, Xin
Format: Article
Language:eng
Subjects:
Amplitudes
Astrophysics
Automotive Engineering
Breathers
Classical Mechanics
Control
Dynamical Systems
Engineering
Fluids
Independent variables
Mechanical Engineering
Oceanography
Original Paper
Solitary waves
Vibration
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Summary:Fluids are studied in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a (3+1)-dimensional Korteweg–de Vries equation in a fluid. Bilinear form and N -soliton solutions are obtained, where N is a positive integer. Via the N -soliton solutions, we derive the higher-order breather solutions. We observe the interaction between the two perpendicular first-order breathers on the x - y and x - z planes and the interaction between the periodic line wave and the first-order breather on the y - z plane, where x , y and z are the independent variables in the equation. We discuss the effects of α , β , γ and δ on the amplitude of the second-order breather, where α , β , γ and δ are the constant coefficients in the equation: Amplitude of the second-order breather decreases as α increases; amplitude of the second-order breather increases as β increases; amplitude of the second-order breather keeps invariant as γ or δ increases. Via the N -soliton solutions, hybrid solutions comprising the breathers and solitons are derived. Based on the Riemann theta function, we obtain the periodic-wave solutions, and find that the periodic-wave solutions approach to the one-soliton solutions under a limiting condition.
ISSN:0924-090X
1573-269X