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 Schrödinger 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.
Publié le : 2004-07-05
Classification:
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech],
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
@article{hal-00146097,
author = {Cherniha, Roman and Henkel, Malte},
title = {On nonlinear partial differential equations with an infinite-dimensional conditional symmetry},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00146097}
}
Cherniha, Roman; Henkel, Malte. On nonlinear partial differential equations with an infinite-dimensional conditional symmetry. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00146097/