Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system

Gao, Xin-Yi; Guo, Yong-Jiang; Shan, Wen-Rui

doi:10.1016/j.chaos.2021.110875

Cited by 45 publications

(10 citation statements)

References 75 publications

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“…Non-linear phenomena are widespread in the life of the world, such as marine engineering, hydrodynamics, chemical physics, etc [1][2][3]. To investigate exact solutions of any complex non-linear partial differential equations and examine the behavior of the solutions is very interesting.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Yang

Song²,

Wang³

2023

Front. Phys.

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In this article, (3+1)-dimensional generalized Shallow Water-like (gSWl) equation is discussed. The infinitesimal generators of the equation are derived by using the Lie symmetry analysis method. The optimal system is obtained based on the adjoint table of the generators of the equation. Exact solutions of the equation are constructed by applying symmetry reduction, Exp−ϕ(ξ) expansion method, Exp-function expansion method, Riccati equation method, and G′/G expansion method. For analyzing the dynamical behavior of the solutions, we derive the physical structures of dark soliton, kink wave, and periodic solutions via numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Yang

Song²,

Wang³

2023

Front. Phys.

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“…Numerous forms of NLEEs are used to explain SWWs, such as the Korteweg-de Vries equation for long shallow water gravity waves [17], the Boussinesq-Burgers system for SWWs on an ocean beach or in a lake [18], and the perturbed Boussinesq equation (PBE) for the solution interaction mechanism of SWWs. All of these equations have one thing in common, they all accommodate soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

Murtaza

Raza

Arshed

2023

Commun. Theor. Phys.

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This paper investigates the perturbed Boussinesq equation that emerges in shallow water waves.The perturbed Boussinesq equation describes the properties of longitudinal waves in bars, long water waves, plasma waves, quantum mechanics, acoustic waves, nonlinear optics, and other phenomena. As a result, the governing model has significant importance in its own right. The singular manifold method and the unified methods are employed in the proposed model for extracting hyperbolic, trigonometric, and rational function solutions. These solutions may be useful in determining the underlying context of the physical incidents. It is worth noting thatthe executed methods are skilled and effective for examining nonlinear evaluation equations, is compatible with computer algebra, and provides a wide range of wave solutions. In addition to this, the Painlev´e test is also used to check the integrability of the governing model. Two dimensional (2D) and three-dimensional (3D) plots are made to illustrate the physical behavior of the newly obtained exact solutions.This makes the study of exact solutions to other nonlinear evaluation equations using the singular manifold method and unified technique prospective and deserving of further study.

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“…Obtaining the exact solutions for nonlinear partial differential equations (PDEs) [1][2][3][4][5][6][7][8][9] have captured the attention of numerous researchers, where they have made use of several methodical approaches to achieve the analytic solutions for nonlinear PDEs as multiple solitons, breather, lump solution, kink solitary wave, rogue wave, and others. In recent years, a wide range of techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been established to understand the different aspects of these analytic solutions such as the Hirota bilinear method, Darboux transformation, simplified Hirota method, Bäcklund transformation, Lie symmetry analysis, Pfaffian technique, Inverse scattering method, and several other methods.…”

Section: Introductionmentioning

confidence: 99%

“…Various novel forms of nonlinear PDEs [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] have arisen over time, each with distinctive features in soliton theory to learn about their characteristics and features. Also, new concepts and theories are being implemented in order to produce substantial results.…”

Section: Introductionmentioning

confidence: 99%

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

2022

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This research aims to investigate a generalized fifth-order nonlinear partial differential equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to study the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasma physics and other nonlinear sciences. The Painlev\'e analysis is used to determine the integrability of the equation, and the simplified Hirota technique is applied to construct multiple soliton solutions with an investigation of the dispersion relation and phase shift of the equation. We utilize a linear combination approach to construct a system of equations to obtain a general logarithmic transformation for dependent variable. We generate one-soliton, two-soliton, and three-soliton wave solutions using the simplified Hirota method and showcase the dynamics of these solutions graphically through interaction between one, two, and three solitons. We investigate the impact of the system's parameters on the solitons and periodic waves. The SK, Lax, and CDG equations have a wide range of applications in nonlinear dynamics, plasma physics, oceanography, soliton theory, fluid dynamics, and other sciences.

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Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system

Cited by 45 publications

References 75 publications

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Lie symmetry analysis and exact solutions of the (3+1)-dimensional generalized Shallow Water-like equation

Painlevé integrability and a collection of new wave structures related to an important model in shallow water waves

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

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