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We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are…

Mathematical Physics · Physics 2019-12-04 Stavros Kontogiorgis , Roman O. Popovych , Christodoulos Sophocleous

Using advanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form $u_t+uu_x+f(t,x)u_{xx}=0$. This enhances all the previous results on symmetries of these…

Mathematical Physics · Physics 2017-12-19 Oleksandr A. Pocheketa , Roman O. Popovych

The (2+1)-dimensional Burgers equation has been investigated first from prospective of symmetry by localizing the nonlocal residual symmetries and then studied by a simple generalized tanh expansion method. New symmetry reduction solutions…

Exactly Solvable and Integrable Systems · Physics 2013-10-02 Xi-zhong Liu , Jun Yu , Bo Ren

In this paper, the new (2+1)-dimensional Burgers equation has been derived using the Burgers equation' recursion operator as follows \begin{equation*} u_{xt}+\left(u_{t}+uu_{x}-\nu…

Exactly Solvable and Integrable Systems · Physics 2023-09-29 Nardjess Benoudina , Nassim Bessaad

Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…

Exactly Solvable and Integrable Systems · Physics 2014-06-24 Oleksandr A. Pocheketa , Roman O. Popovych , Olena O. Vaneeva

The symmetry classification of the two dimensional Burgers equation with variable coefficient is considered. Symmetry algebra is found and a classification of its subalgebras, up to conjugacy, is obtained. Similarity reductions are…

Exactly Solvable and Integrable Systems · Physics 2010-03-15 D. Pandiaraja , B. Mayil Vaganan

We consider a class of variable coefficient Burgers equations in 2+1 dimensions and make use of their equivalence group to give a complete symmetry classification up to equivalence. Equivalence group is also applied to pick out the most…

Exactly Solvable and Integrable Systems · Physics 2014-02-13 F. Güngör , C. Özemir

Among Lie submodels of the (real symmetric potential) dispersionless Nyzhnyk equation, we single out a remarkable submodel as such that, despite being the only one, is associated with a family of in general inequivalent one-dimensional…

Mathematical Physics · Physics 2026-01-16 Oleksandra O. Vinnichenko , Vyacheslav M. Boyko , Roman O. Popovych

We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that the pseudogroup of these transformations has exactly two connected…

Analysis of PDEs · Mathematics 2024-09-19 Serhii D. Koval , Roman O. Popovych

The topic of this paper are similarity solutions occurring in multi-dimensional Burgers' equation. We present a simple derivation of the symmetries appearing in a family of generalizations of Burgers' equation in $d$-space dimensions. These…

Numerical Analysis · Mathematics 2017-12-06 Jens Rottmann-Matthes

A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method of construction of exact solutions, based on a class of…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 M. Rudnev , A. V. Yurov , V. A. Yurov

In this paper, the initial value problem of the convection-diffusion equation of Burgers type is treated. In the asymptotic profile of solutions, the nonlinearity of the equation is reflected. Regarding the solutions to this model, the…

Analysis of PDEs · Mathematics 2025-10-30 Masakazu Yamamoto

Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and…

Analysis of PDEs · Mathematics 2024-06-06 Dmytro R. Popovych , Alex Bihlo , Roman O. Popovych

We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal…

Mathematical Physics · Physics 2008-04-24 Valentyn Tychynin , Olga Petrova , Olesya Tertyshnyk

A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…

Analysis of PDEs · Mathematics 2020-04-23 Roman Cherniha , Mykola Serov , Yulia Prystavka

In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the…

Analysis of PDEs · Mathematics 2014-09-22 Manoj Gaur , K. Singh

In this article we study generalizations of the inhomogeneous Burgers equation. First at the operator level, in the sense that we replace classical differential derivations by operators with certain properties, and then we increase the…

Analysis of PDEs · Mathematics 2024-11-08 Francesco Maltese

Two-component second and third-order Burgers type systems with nondiagonal constant matrix of leading order terms are classified for higher symmetries. New symmetry integrable systems with their master symmetries are obtained. Some third…

Exactly Solvable and Integrable Systems · Physics 2016-05-04 D. Talati , R. Turhan

Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…

Analysis of PDEs · Mathematics 2012-08-08 Philippe G. LeFloch , Hasan Makhlof , Baver Okutmustur

We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible…

Mathematical Physics · Physics 2008-03-07 Roman O. Popovych , Michael Kunzinger , Nataliya M. Ivanova
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