Journal of Nonlinear Mathematical Physics

Volume 6, Issue 4, November 1995, Pages 355 - 364

Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation

Authors
Christodoulos SOPHOCLEOUS
Corresponding Author
Christodoulos SOPHOCLEOUS
Available Online 1 November 1995.
DOI
https://doi.org/10.2991/jnmp.1999.6.4.1How to use a DOI?
Abstract
We consider the one-dimensional porous medium equation ut = (un ux)x + µ x un ux. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial differential equation can be equivalently written as a system of two equations. Point transformations are also sought for this auxiliary system. It turns out that in addition to the continuous point transformations that may be derived by Lie's method, a number of discrete transformations are obtained. In some cases the point transformations which are presented here for the single equation and for the auxiliary system form cyclic groups of finite order.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 4
Pages
355 - 364
Publication Date
1995/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.4.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Christodoulos SOPHOCLEOUS
PY  - 1995
DA  - 1995/11
TI  - Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 355
EP  - 364
VL  - 6
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.4.1
DO  - https://doi.org/10.2991/jnmp.1999.6.4.1
ID  - SOPHOCLEOUS1995
ER  -