On nonlinear partial differential equations with an infinite-dimensional conditional symmetry
Abstract
The invariance of nonlinear partial differential equations under a certain infinite-dimensional Lie algebra A_N(z) in N spatial dimensions is studied. The special case A_1(2) was introduced in J. Stat. Phys. {\bf 75}, 1023 (1994) and contains the Schr\"odinger Lie algebra sch_1 as a Lie subalgebra. It is shown that there is no second-order equation which is invariant under the massless realizations of A_N(z). However, a large class of strongly non-linear partial differential equations is found which are conditionally invariant with respect to the massless realization of A_N(z) such that the well-known Monge-Ampere equation is the required additional condition. New exact solutions are found for some representatives of this class.
Cite
@article{arxiv.math-ph/0402059,
title = {On nonlinear partial differential equations with an infinite-dimensional conditional symmetry},
author = {Roman Cherniha and Malte Henkel},
journal= {arXiv preprint arXiv:math-ph/0402059},
year = {2007}
}
Comments
Latex2e, 14 pages, no figures; final form