# Lie symmetries of generalized Burgers equations: application to boundary-value problems

@article{Vaneeva2013LieSO, title={Lie symmetries of generalized Burgers equations: application to boundary-value problems}, author={Olena O. Vaneeva and Christodoulos Sophocleous and Peter G. L. Leach}, journal={Journal of Engineering Mathematics}, year={2013}, volume={91}, pages={165-176} }

There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. Using an example of generalized Burgers equations appearing in non-linear acoustics we show that the direct procedure of solving boundary-value problems using Lie symmetries first described by Bluman is more general and straightforward than the method suggested by Moran and…

## 20 Citations

Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries

- Mathematics, Computer ScienceCommun. Nonlinear Sci. Numer. Simul.
- 2014

The found Lie symmetries are applied in order to reduce the initial and boundary value problem for the generalized KdV equations to an initialvalue problem for nonlinear third-order ODEs.

Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2014

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…

Lie symmetry analysis of some conformable fractional partial differential equations

- Mathematics, PhysicsArabian Journal of Mathematics
- 2018

In this article, Lie symmetry analysis is used to investigate invariance properties of some nonlinear fractional partial differential equations with conformable fractional time and space derivatives.…

Enhanced symmetry analysis of two-dimensional degenerate Burgers equation

- Mathematics, Physics
- 2019

We carry out enhanced symmetry analysis of a two-dimensional degenerate Burgers equation. Its complete point-symmetry group is found using the algebraic method, and its generalized symmetries are…

SYMMETRIES AND EXACT SOLUTIONS OF CONFORMABLE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

- Mathematics
- 2020

In this paper Lie group analysis is used to investigate invariance properties of
nonlinear fractional partial differential equations with conformable fractional time derivative.
The analysis is…

Lie Group Classification for a Class of Compound KdV–Burgers Equations with Time-Dependent Coefficients

- Mathematics
- 2020

We derive the Lie group classification for a general class of KdV–Burgers equations, where the coefficients are functions of time. We demonstrate how important is the use of equivalence…

Group analysis of general Burgers–Korteweg–de Vries equations

- Mathematics, Physics
- 2017

The complete group classification problem for the class of (1+1)-dimensional rth order general variable-coefficient Burgers–Korteweg–de Vries equations is solved for arbitrary values of r greater…

Group Classification and Conservation Laws of a Class of Hyperbolic Equations

- MathematicsAbstract and Applied Analysis
- 2021

Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing…

Enhanced group classification of nonlinear diffusion–reaction equations with gradient-dependent diffusivity

- Mathematics, Physics
- 2020

Abstract We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion–reaction equations with gradient-dependent diffusivity using the two-step version of the…

Lie symmetries of a generalized Kuznetsov–Zabolotskaya–Khokhlov equation

- Mathematics
- 2015

Abstract We consider a class of generalized Kuznetsov–Zabolotskaya–Khokhlov (gKZK) equations and determine its equivalence group, which is then used to give a complete symmetry classification of this…

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