Integration of PDEs by differential geometric means
Differential Geometry
2013-02-25 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We use Vessiot theory and exterior calculus to solve partial differential equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated evolution equations. These equations are represented by the Vessiot distribution of vector fields. We develop and apply an algorithm to find the largest integrable sub-distributions and hence solutions of the PDEs. We then apply the integrating factor technique [19] to integrate this integrable Vessiot sub-distribution. The method is successfully applied to a large class of linear and non-linear PDEs.
Keywords
Cite
@article{arxiv.1302.5562,
title = {Integration of PDEs by differential geometric means},
author = {Naghmana Tehseen and Geoff Prince},
journal= {arXiv preprint arXiv:1302.5562},
year = {2013}
}