Lie group analysis of two-dimensional variable-coefficient Burgers equation

Иванова, Н. М.; Sophocleous, Christodoulos; Tracinà, Rita

doi:10.1007/s00033-009-0053-8

Cited by 18 publications

(12 citation statements)

References 29 publications

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“…The Einstein summation convention is adopted in (7), (8) and (9). The invariance condition (6) yields an over-determined system of linear partial differential equations (determining equations) for the symmetry group of equation 5.…”

Section: Preliminariesmentioning

confidence: 99%

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Symmetry Reductions and Invariant Solutions of a Nonlinear Fokker-Planck Equation Based on the Sharma-Taneja-Mittal Entropy

Sinkala¹

2020

Int. J. of Appl. Math.

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Section: Preliminariesmentioning

confidence: 99%

“…Numerous other papers have been devoted to group classification of diverse differential equations. In particular, many classes of nonlinear evolution equations depending on arbitrary functions of one, or at most two, variables have been studied via this method [3,9,7,8,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Symmetry Reductions and Invariant Solutions of a Nonlinear Fokker-Planck Equation Based on the Sharma-Taneja-Mittal Entropy

Sinkala¹

2020

Int. J. of Appl. Math.

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“…Sahin et al [11] investigated the selfsimilarity solutions of the one-layer shallow-water equations representing gravity currents using Lie group analysis. Two-dimensional generalization of the Burgers equation, using Lie group analysis, has been discussed by Ivanova et al [12]. Lie group analysis and basic similarity reductions are performed for MHD aligned creeping flow and heat transfer in a second-grade fluid by neglecting the inertial terms by Afify [13].…”

Section: Introductionmentioning

confidence: 99%

Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics

Bira

Sekhar

2014

Applicable Analysis

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The aim of this paper is to carry out symmetry group analysis to obtain important classes of exact solutions from the given system of nonlinear partial differential equations (PDEs). Lie group analysis is employed to derive some exact solutions of one dimensional unsteady flow of an ideal isentropic, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field for the magnetogasdynamics system. By using Lie group theory, the full one-parameter infinitesimal transformations group leaving the equations of motion invariant is derived. The symmetry generators are used for constructing similarity variables which leads the system of PDEs to a reduced system of ordinary differential equations; in some cases, it is possible to solve these equations exactly. Further, using the exact solution, we discuss the evolutionary behavior of weak discontinuity.

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“…In fact, transformations are perhaps the most powerful tool currently available in this area [12][13][14]. Ivanova, Sophocleous and Tracin in [15] investigated the Lie symmetry analysis of (2+1) -dimensional variable coefficient Burgers differential equation of the form u t = A(t)u xx + B(t)u yy + uu x .…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers' Differential Equation

Iskenderoglu

Kaya

2019

Fundamental Journal of Mathematics and Applications

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Many physical phenomena in nature can be described or modeled via a differential equation or a system of differential equations. In this work, we restrict our attention to research a solution of fractional nonlinear generalized Burgers' differential equations. Thereby we find some exact solutions for the nonlinear generalized Burgers' differential equation with a fractional derivative, which has domain as R 2 × R + . Here we use the Lie groups method. After applying the Lie groups to the boundary value problem we get the partial differential equations on the domain R 2 with reduced boundary and initial conditions. Also, we find conservation laws for the nonlinear generalized Burgers' differential equation.They obtained the symmetries, according them conservation laws and some analytical solutions for above equation. Later Abd-el-Malek and Amin in [16] studied the symmetry analysis of the generalized (1+1)-dimensional Burgers differential equation in the formwith boundary and initial conditions u(0, x) −→ ∞, for x > 0, u(t, 0) = γr(t), for t > 0, γ = 0, and lim x→∞ u(t, x) −→ ∞, for t > 0.Some recent studies of Burgers differential equation the reader can see in [17,18]. In this research, we show the applying of Lie group analysis to study (2+1)-dimensional time-fractional generalized Burgers' differential equation with boundary and initially conditions:Email addresses and ORCID numbers: gulistan.iskandarova@istanbulticaret.edu.tr, https://orcid.org/0000-0001-7322-1339 (G. Iskenderoglu), dogank@ticaret.edu.tr, https://orcid.org/0000-0002-3420-7718 (D. Kaya)

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Lie group analysis of two-dimensional variable-coefficient Burgers equation

Cited by 18 publications

References 29 publications

Symmetry Reductions and Invariant Solutions of a Nonlinear Fokker-Planck Equation Based on the Sharma-Taneja-Mittal Entropy

Symmetry Reductions and Invariant Solutions of a Nonlinear Fokker-Planck Equation Based on the Sharma-Taneja-Mittal Entropy

Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics

Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers' Differential Equation

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