Study of exact analytical solutions and various wave profiles of a new extended (2+1)-dimensional Boussinesq equation using symmetry analysis

Kumar, Sachin; Rani, Setu

doi:10.1016/j.joes.2021.10.002

Cited by 33 publications

(5 citation statements)

References 40 publications

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“…The Lie symmetries, a one-dimensional optimal system and symmetry reductions of the nonlinear systems are presented in a systematic review [27][28][29]. The explicit solutions are obtained by solving the related characteristics equations.…”

Section: Similarity Reductions Of Kdvskr Equationmentioning

confidence: 99%

“…The multi-solitary waves of the non-autonomous Zakharov-Kuznetsov equation are studied by utilizing Hirota's bilinear method [33]. Based on the Lie point symmetry method, the dynamical behaviors of the invariant solutions are discussed through three-and twodimensional profiles [27][28][29]. Here one demonstrates the invariant solution graphically in case III.…”

Section: Similarity Reductions Of Kdvskr Equationmentioning

confidence: 99%

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Painlevé analysis, infinite dimensional symmetry group and symmetry reductions for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Ren

Lin

Wang

2023

Commun. Theor. Phys.

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The (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani (KdVSKR) equation is studied by the singularity structure analysis. It is proved that it admits the Painleve property. The Lie algebras which depend on three arbitrary functions of time t are obtained by the Lie point symmetry method. It is shown that the KdVSKR equation possesses an infinite-dimensional Kac-Moody-Virasoro symmetry algebra. By selecting first-order polynomials in t, a finite-dimensional subalgebra of physical transformations is studied. The commutation relations of the subalgebra which have been established by selecting the Laurent polynomials in t are calculated. This symmetry constitutes a centerless Virasoro algebra which has been widely used to the field of physics. In the meanwhile, the similarity reduction solutions of the model are studied by means of the Lie point symmetry theory.

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Section: Similarity Reductions Of Kdvskr Equationmentioning

confidence: 99%

Section: Similarity Reductions Of Kdvskr Equationmentioning

confidence: 99%

Painlevé analysis, infinite dimensional symmetry group and symmetry reductions for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Ren

Lin

Wang

2023

Commun. Theor. Phys.

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“…The substitution of the equations ( 17), (22), and (23) into equation (12), results in two-soliton solution of equation (4).…”

Section: Two-soliton Solutionmentioning

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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“…Through this method, an analytic form of solution is obtained, which might be very useful in classifying and analyzing the non-linear phenomenon involved. In this sequence, we would like to mention the work presented in previous studies [27][28][29][30][31][32][33] in which analytic solutions were obtained for different fluid-flow models using Lie symmetry analysis, which is also a convenient method for obtaining closed-form solutions. The power series approach may be used to find solutions of any needed degree of accuracy; yet, the required computations involve a great deal of work.…”

Section: Introductionmentioning

confidence: 99%

An analysis of shock wave propagation in a dusty gas

Singh

Arora

2022

Math Methods in App Sciences

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The present work uses a power series method to investigate the propagation of shock waves with generalized geometries generated by an intense explosion in a dusty gas. A mathematical model using a system of partial differential equations (PDEs) is presented for the considered problem. The density of the undisturbed medium is assumed to be constant. Approximate analytic solutions to the considered problem are obtained using the power series method by extending the power series of the flow variables. This work discusses the first‐order and second‐order approximate solutions and provides closed‐form solutions for the first‐order approximation. The behavior of the flow variables is depicted via figures behind the shock front for the first‐order approximation. Furthermore, the effects of geometry factor α, adiabatic exponent γ, and various dusty gas parameters such as Kp (the mass fraction of the dust particles), G0 (the ratio of the density of the dust particles to the initial density of the gas), and σ (the relative specific heat) are analyzed on the flow variables and total energy of disturbance J0 for the first‐order approximation. It is observed that an increase in any of the parameters Kp or σ causes the fluid velocity to increase and density and pressure to decrease. Increase in the parameter G0 causes the density and pressure to increase, whereas the fluid velocity does not get affected. An increase in the value of α results in a decrease in the density and pressure, while the fluid velocity remains the same. An increase in the value of γ results in a decrease in the fluid velocity; however, it has opposite effect on the pressure. The density decreases near the shock front and increases as we move towards the axis/center of symmetry with an increase in γ. Also, it is observed that J0 increases on increasing the value of G0 or σ, while it decreases on increasing the value of Kp, γ or α.

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Study of exact analytical solutions and various wave profiles of a new extended (2+1)-dimensional Boussinesq equation using symmetry analysis

Cited by 33 publications

References 40 publications

Painlevé analysis, infinite dimensional symmetry group and symmetry reductions for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Painlevé analysis, infinite dimensional symmetry group and symmetry reductions for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

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

An analysis of shock wave propagation in a dusty gas

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