Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equation

Chauhan, Astha; Sharma, Kajal; Arora, Rajan

doi:10.1002/mma.6547

Cited by 36 publications

(13 citation statements)

References 33 publications

(42 reference statements)

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“…Motivated by the reasons above, there are several papers essentially analysing the Lie symmetries of PDEs. [13][14][15][16] Specifically, by using the Lie symmetry method, symmetries can be used to find exact invariant solutions.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation

Márquez

Garrido

Recio

et al. 2022

Math Methods in App Sciences

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In this paper, we consider a fourth-order nonlinear diffusion partial differential equation, depending on two arbitrary functions. First, we perform an analysis of the symmetry reductions for this parabolic partial differential equation by applying the Lie symmetry method. The invariance property of a partial differential equation under a Lie group of transformations yields the infinitesimal generators. By using this invariance condition, we present a complete classification of the Lie point symmetries for the different forms of the functions that the partial differential equation involves. Afterwards, the optimal systems of one-dimensional subalgebras for each maximal Lie algebra are determined, by computing previously the commutation relations, with the Lie bracket operator, and the adjoint representation. Next, the reductions to ordinary differential equations are derived from the optimal systems of one-dimensional subalgebras.Furthermore, we study travelling wave reductions depending on the form of the two arbitrary functions of the original equation. Some travelling wave solutions are obtained, such as solitons, kinks and periodic waves.

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Section: Introductionmentioning

confidence: 99%

Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation

Márquez

Garrido

Recio

et al. 2022

Math Methods in App Sciences

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“…Authors 38,39 also made a complete group classification of the fourth‐ and the fifth‐order KdV equations. Chauhan et al 40 presented the Lie symmetry analysis and explicit series solutionto the Date–Jimbo–Kashiwara–Miwa equation. Singla and Gupta 41 extended the symmetry approach from single‐time FPDEs to nonlinear system of time FODEs.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws and exact series solution of fractional‐order Hirota–Satsuma‐coupled Korteveg–de Vries system by symmetry analysis

Gandhi

Tomar

Singh

2021

Math Methods in App Sciences

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The main goal of the paper is to obtain invariance analysis of fractional-order Hirota-Satsuma-coupled Korteveg-de Vries (HSC-KdV) system of equations based on Riemann-Liouville (RL) derivatives. The Lie symmetry analysis is considered to obtain infinitesimal generators; we reduced the system of coupled equations into nonlinear fractional ordinary differential equations (FODEs) with the help of Erdelyi-Kober (EK) fractional differential and integral operators. The reduced system of FODEs was solved by means of power series technique with its convergence. The conservation laws of the system were constructed by the Noether's theorem.

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“…Among those methods, the Lie symmetry analysis method is an algorithmic approach that provides an efficient tool to construct an exact solution of FDEs in a systematic way. Initially, this method was proposed by Norwegian mathematician Sophus Lie during the 19th century and was further developed by Ovsianikov [49] and others [5,10,27,31,34,38,[46][47][48]56,62]. The Lie symmetry analysis method is to find continuous transformations of one or more parameters leaving the differential equation invariant in the new coordinate system wherein the resulting differential equation is easier to solve.…”

Section: Introductionmentioning

confidence: 99%

On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations

Sethukumarasamy¹,

Vijayaraju²,

Prakash³

2021

JNMP

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In this article, we explain how to extend the Lie symmetry analysis method for n-coupled system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. Also, we systematically investigated how to derive Lie point symmetries of scalar and coupled fractional ordinary differential equations namely (i) fractional Thomas-Fermi equation, (ii) Bagley-Torvik equation, (iii) two-coupled system of fractional quartic oscillator, (iv) fractional type coupled equation of motion and (v) fractional Lotka-Volterra ABC system.The dimensions of the symmetry algebras for the Bagley-Torvik equation and its various cases are greater than 2 and for this reason we construct optimal system of one-dimensional subalgebras. In addition, the exact solutions of the above mentioned fractional ordinary differential equations are explicitly derived wherever possible using the obtained symmetries.

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Lie symmetry analysis, optimal system, and generalized group invariant solutions of the (2 + 1)‐dimensional Date–Jimbo–Kashiwara–Miwa equation

Cited by 36 publications

References 33 publications

Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation

Lie symmetries and exact solutions for a fourth‐order nonlinear diffusion equation

Conservation laws and exact series solution of fractional‐order Hirota–Satsuma‐coupled Korteveg–de Vries system by symmetry analysis

On Lie Symmetry Analysis of Certain Coupled Fractional Ordinary Differential Equations

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