Journal of Ocean Engineering and Science, 2022 This study deals with a new (3 + 1) dimensional Hirota equation that emerges in shallow water waves theory. Considering the bilinear form of this equation, the bilinear neural network method was applied.
Yaşar E., Zeynel M.
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Results in Physics, 2023 The purpose of this research paper is to investigate the (3+1)-dimensional Hirota bilinear equation that arises in nonlinear waves in fluid dynamics, plasma physics and shallow water waves.
Hajar F. Ismael +5 more
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A diversity of patterns to new (3 + 1)-dimensional Hirota bilinear equation that models dynamics of waves in fluids [PDF]
Results in Physics, 2023 This article discusses the behavior of specific dispersive waves to new (3+1)-dimensional Hirota bilinear equation (3D-HBE). The 3D-HBE is used as a governing equation for the propagation of waves in fluid dynamics.
U. Younas +5 more
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On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions [PDF]
Heliyon, 2023 In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method.
Baoyong Guo, Yong Fang, Huanhe Dong
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Analytical Treatment of the Generalized Hirota-Satsuma-Ito Equation Arising in Shallow Water Wave
Advances in Mathematical Physics, 2021 In the current study, an analytical treatment is studied starting from the 2+1-dimensional generalized Hirota-Satsuma-Ito (HSI) equation. Based on the equation, we first establish the evolution equation and obtain rational function solutions by means of ...
Fan Yong-Yan +4 more
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Exact breather waves solutions in a spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions [PDF]
Scientific ReportsIn this article, the spatial symmetric nonlinear dispersive wave model in (2+1)-dimensions is studied, which have many applications in wave phenomena and soliton interactions in a two-dimensional space with time.
Qunyan Zou +6 more
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Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation [PDF]
Advances in Mathematical Physics, 2015 The relations between Dp-operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms with Dp-operators of nonlinear equations directly and quickly.
Jingzhu Wu, Xiuzhi Xing, Xianguo Geng
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Combined Exp-Function Ansatz Method and Applications [PDF]
Abstract and Applied Analysis, 2013 Our aim is to present a combined Exp-function ansatz method. This method replaces the traditional assumptions of multisolitons by a combination of the hyperbolic functions and triangle functions in Hirota bilinear forms of nonlinear evolution equation ...
Gui Mu, Jun Liu, Zhengde Dai, Xi Liu
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Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation [PDF]
Abstract and Applied Analysis, 2014 We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1)-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials ...
Huanhe Dong +3 more
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Soliton solutions by means of Hirota bilinear forms
Partial Differential Equations in Applied Mathematics, 2022 The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various ...
Wen-Xiu Ma
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