Wronskian, Gramian, Pfaffian and periodic-wave solutions for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Application of the shallow water waves in environmental engineering and hydraulic engineering is seen. In this paper, a (3+1)-dimensional generalized nonlinear evolution equation (gNLEE) for the shallow water waves is investigated. The N th-order Wronskian, Gramian and Pfaffian solutions are proved,...

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Bibliographic Details
Published in:Nonlinear dynamics 2022-04, Vol.108 (2), p.1599-1616
Main Authors: Liu, Fei-Yan, Gao, Yi-Tian, Yu, Xin, Ding, Cui-Cui
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Environmental engineering
Hydraulic engineering
Mechanical Engineering
Nonlinear evolution equations
Original Paper
Qualitative analysis
Shallow water
Solitary waves
Vibration
Water waves
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Summary:Application of the shallow water waves in environmental engineering and hydraulic engineering is seen. In this paper, a (3+1)-dimensional generalized nonlinear evolution equation (gNLEE) for the shallow water waves is investigated. The N th-order Wronskian, Gramian and Pfaffian solutions are proved, where N is a positive integer. Soliton solutions are constructed from the N th-order Wronskian, Gramian and Pfaffian solutions. Moreover, we analyze the second-order solitons with the influence of the coefficients in the equation and illustrate them with graphs. Through the Hirota-Riemann method, one-periodic-wave solutions are derived. Relationship between the one-periodic-wave solutions and one-soliton solutions is investigated, which shows that the one-periodic-wave solutions can approach to the one-soliton solutions under certain conditions. We reduce the (3+1)-dimensional gNLEE to a two-dimensional planar dynamic system. Based on the qualitative analysis, we give the phase portraits of the dynamic system.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-022-07249-1