# Exact solutions to the equations of perfect gases through Lie group analysis and substitution principles

@article{Oliveri1999ExactST, title={Exact solutions to the equations of perfect gases through Lie group analysis and substitution principles}, author={Francesco Oliveri and M. P. Speciale}, journal={International Journal of Non-linear Mechanics}, year={1999}, volume={34}, pages={1077-1087} }

## 32 Citations

Group analysis of three dimensional Euler equations of gas dynamics

- Mathematics, Physics
- 2009

In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are performed. Reduced…

New class of symmetries and exact solution to the unsteady equations of adiabatic gas dynamics

- Mathematics, Physics
- 2005

Similarity solutions for three dimensional Euler equations using Lie group analysis

- MathematicsAppl. Math. Comput.
- 2008

Exact solutions of Euler equations of ideal gasdynamics via Lie group analysis

- Mathematics
- 2008

Abstract.In this paper, we explicitly characterize a class of solutions to the first order quasilinear system of partial differential equations (PDEs), governing one dimensional unsteady planar and…

Lie Symmetries of Differential Equations: Classical Results and Recent Contributions

- MathematicsSymmetry
- 2010

This paper reviews some well known results of Lie group analysis, as well as some recent contributions concerned with the transformation of differential equations to equivalent forms useful to investigate applied problems.

Exact solutions to magnetogasdynamics using Lie point symmetries

- Mathematics
- 2013

In the present work, we find some exact solutions to the first order quasilinear hyperbolic system of partial differential equations (PDEs), governing the one dimensional unsteady flow of inviscid…

Similarity reduction and closed form solutions for a model derived from two-layer fluids

- Mathematics
- 2013

In this paper, we study an integrable system of coupled KdV equations, derived by Gear and Grimshaw (Stud. Appl. Math. 70(3):235-258, 1984), modeling the strong interaction of two-dimensional, long,…

Classification of Similarity Solutions for Inviscid Burgers’ Equation

- Mathematics
- 2010

Abstract.Using the basic Lie symmetry method, we find the most general Lie point symmetries group of the inviscid Burgers’ equation. Looking at the adjoint representation of the obtained symmetry…

Symmetries and exact solutions of the rotating shallow-water equations

- Mathematics, PhysicsEuropean Journal of Applied Mathematics
- 2009

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the…

Lie symmetries of differential equations:direct and inverse problems

- Mathematics
- 2004

This paper reviews some relevant problems arising within the context of Lie group analysis of dieren tial equations either in the direct approach or in the inverse one. For what concerns the direct…

## References

SHOWING 1-10 OF 20 REFERENCES

On the equations of ideal-gas dynamics with a separable equation of state: Lie group analysis and substitution principles

- Mathematics
- 1992

Exact solutions to the equations of ideal gas-dynamics by means of the substitution principle

- Mathematics
- 1998

Galilean Quasilinear Systems of PDE’s and the Substitution Principle

- Mathematics
- 1993

The quasilinear systems of partial differential equations which are invariant with respect to the celebrated Galilean group of transformations are characterized by means of Lie group analysis.…

Reduction to autonomous form by means of canonical variables

- Mathematics
- 2000

In this paper it is shown to transform to autonomous form a general nonautonomous system of partial differential equations in n independent variables provides it is left invariant by n Lie groups of…

Direct reduction and differential constraints

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- 1994

Direct reductions of partial differential equations to systems of ordinary differential equations are in one-to-one correspondence with compatible differential constraints. The differential…

Linearization Procedure of Nonlinear First Order System of Partial Differential Equations by Means of Canonical Variables Related to Lie Groups of Point Transformations

- Mathematics
- 1994

an algorithm is given to linearize nonlinear first order systems of partial differential equations admitting an infinite-parameter lie group of point trasformations. The associated infinitesimal…

How to build up variable transformations allowing one to map nonlinear hyperbolic equations into autonomous or linear ones

- Mathematics
- 1996

The paper claims to give a systematic approach allowing one to obtain invertible variable transformations mapping nonlinear partial differential equations either into autonomous or linear form…

When nonautonomous equations are equivalent to autonomopus ones

- Mathematics
- 1995

We consider nonlinear systems of first order partial differential equations admitting at least two one-parameter Lie groups of transformations with commuting infinitesimal operators. Under suitable…

Equivalence, invariants, and symmetry

- Mathematics
- 1995

1. Geometric foundations 2. Lie groups 3. Representation theory 4. Jets and contact transformations 5. Differential invariants 6. Symmetries of differential equations 7. Symmetries of variational…

When Nonlinear Differential Equations are Equivalent to Linear Differential Equations

- Mathematics
- 1982

A necessary and sufficient condition is established for the existence of a 1-1 transformation of a system of nonlinear differential equations to a system of linear equations. The obtained theorems…