3D solutions of non-linear evolution equations with diffusion

Publisher Website
Google Scholar
Abstract
A new technique is developed to solve for the first time non-linear evolution equations with diffusion. The results, which are obtained by means of a generating function and an associated operator, are expressed in a general form which explicitly refers to a double elliptically deformed spherical case. Solutions to cases of lower dimensionality or of higher symmetry can be directly found as special cases of this general form. The solutions, which correspond to physically realistic initial conditions are exact in the radially symmetric spherical and cylindrical cases, as well as in the plane case, whereas in elliptically deformed cases the solutions are valid asymptotically for long times. The relevance of the results for description of recombining diffusive plasmas is discussed

This publication has 0 references indexed in Scilit: