Symmetry Analysis and Some New Exact Solutions of the (2+1)-dimensional Burgers Equations

El-Bialy, F.; Latif, M. S. Abdel; Elsaid, A.

doi:10.5506/aphyspolb.48.2031

Cited by 3 publications

(1 citation statement)

References 26 publications

(39 reference statements)

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“…Many methods have been proposed in the literature for getting exact and approximate solutions to these equations. Examples of these methods are, (G'/G)-expansion method [10,13], generalized F-expansion Method [23], Lie symmetry analysis method [7,8,11,14,19], generalized new auxiliary equation method [10][11], the invariant subspace method [3,4,15], homotopy perturbation methods [9,18], and reproducing Kernel Hilbert Space Method [17].…”

Section: Introductionmentioning

confidence: 99%

Some new exact solutions for a generalized variable coefficients KdV equation

Rajagopalan¹,

Kader²,

Latif³

et al. 2022

J. Math. Computer Sci.

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In this paper, the variable coefficients KdV equation with general power nonlinearities is proposed. Firstly, it is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to transform the obtained constant coefficients generalized KdV equation into a generalized ordinary differential equation. We give a classification for the obtained generalized ordinary differential equation using a suitable integrating factor. Some new solutions are obtained for the generalized KdV equation with constant coefficients. All the obtained solutions in this paper for the variable coefficients KdV equation with general power nonlinearities are new.

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Section: Introductionmentioning

confidence: 99%

Some new exact solutions for a generalized variable coefficients KdV equation

Rajagopalan¹,

Kader²,

Latif³

et al. 2022

J. Math. Computer Sci.

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Some new soliton-like and doubly periodic-like solutions of Fisher equation with time-dependent coefficients

et al. 2018

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The Invariant Subspace Method for Solving Fractional Partial Differential Equations

Latif

Kader

2020

Advanced Applications of Fractional Differential Operators to Science and Technology

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In this chapter, the authors discuss the effectiveness of the invariant subspace method (ISM) for solving fractional partial differential equations. For this purpose, they have chosen a nonlinear time fractional partial differential equation (PDE) with variable coefficients to be investigated through this method. One-, two-, and three-dimensional invariant subspace classifications have been performed for this equation. Some new exact solutions have been obtained using the ISM. Also, the authors give a comparison between this method and the homogeneous balance principle (HBP).

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Symmetry Analysis and Some New Exact Solutions of the (2+1)-dimensional Burgers Equations

Abstract: In this paper, the Lie point symmetry analysis method is used to investigate the (2+1)-dimensional Burgers equations. We have obtained the optimal system of Lie subalgebras. Some new exact solutions for the (2+1)dimensional Burgers equations are obtained.

Cited by 3 publications

References 26 publications

Some new exact solutions for a generalized variable coefficients KdV equation

Some new exact solutions for a generalized variable coefficients KdV equation

Some new soliton-like and doubly periodic-like solutions of Fisher equation with time-dependent coefficients

The Invariant Subspace Method for Solving Fractional Partial Differential Equations

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