Continuous and discrete transformations of a one-dimensional porous medium equation
Date
1999ISSN
1402-9251Source
Journal of Nonlinear Mathematical PhysicsVolume
6Issue
4Pages
355-364Google Scholar check
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We consider the one-dimensional porous medium equation (Formula presented.) 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. © 1999 Taylor & Francis Group, LLC.