Results 51 to 60 of about 111,509 (220)

Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation

International Journal of Differential Equations, 2023
In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative.
Maria Ihsane El Bahi, Khalid Hilal
doaj   +1 more source

Lie-Point Symmetries Preserved by Derivative

Geometry Integrability and Quantization, 2020
Conditions to guarantee that a point symmetry X of an nth-order differential equation q(n) − ω = 0 is simultaneously a point symmetry of its derived equation q(n+1) − ω = 0 are analyzed, and the possible types of vector fields established. It is further shown that only the simple Lie algebra sl(2, R) for a very specific type of realization in the plane
openaire   +2 more sources

ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS

Acta Polytechnica, 2016
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens.
Giorgio Gubbiotti, Decio Levi, Christian Scimiterna   +2 more
doaj   +1 more source

Potential Nonclassical Symmetries and Solutions of Fast Diffusion Equation

, 2006
The fast diffusion equation $u_t=(u^{-1}u_x)_x$ is investigated from the symmetry point of view in development of the paper by Gandarias [Phys. Lett. A 286 (2001) 153-160].
Ivanova, Nataliya M., Popovych, Roman O., Vaneeva, Olena O.   +2 more
core   +3 more sources

Symmetries of nonlinear ordinary differential equations: the modified Emden equation as a case study

, 2015
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries,
Chandrasekar, V. K., Mohanasubha, R., Senthilvelan, M.   +2 more
core   +1 more source

Nonlinear potential filtration equation and global actions of Lie symmetries

Electronic Journal of Differential Equations, 2009
The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action ...
Mark R. Sepanski
doaj  

Some general new Einstein Walker manifolds

, 2012
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold.
Jafari, Mehdi, Nadjafikhah, Mehdi
core   +2 more sources

Heat polynomials and Lie point symmetries

Journal of Mathematical Analysis and Applications, 2006
On the example of the \(1+1\) dimensional heat equation the author develops the generalized procedure of polynomial solutions construction based on the group theoretical properties of the equation.
openaire   +2 more sources

Classification of the Group Invariant Solutions for Contaminant Transport in Saturated Soils under Radial Uniform Water Flows

Advances in Mathematical Physics, 2014
The transport of chemicals through soils to the groundwater or precipitation at the soils surfaces leads to degradation of these resources. Serious consequences may be suffered in the long run.
M. M. Potsane, R. J. Moitsheki
doaj   +1 more source

Group Analysis of Equal-Width Equation

European Journal of Mathematical Analysis, 2023
We study a third-order nonlinear equal width equation, which has been used for simulation of a one-dimensional wave propagation in a non-linear medium with dispersion process, by symmetry analysis.
Joseph Owuor Owino
doaj   +1 more source