On nonlinear partial differential equations with an infinite-dimensional conditional symmetry

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dc.creatorCherniha, Roman
dc.creatorHenkel, Malte
dc.date2004-02-22
dc.date2004-10-08
dc.date.accessioned2026-07-07T04:30:58Z
dc.date.available2026-07-07T04:30:58Z
dc.descriptionThe 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.
dc.descriptionLatex2e, 14 pages, no figures; final form
dc.identifierhttps://arxiv.org/abs/math-ph/0402059
dc.identifierhttp://arxiv.org/abs/math-ph/0402059
dc.identifierJ. Math. Anal. Appl. 298, 487-500 (2004)
dc.identifierdoi:10.1016/j.jmaa.2004.05.038
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57659
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectAnalysis of PDEs
dc.titleOn nonlinear partial differential equations with an infinite-dimensional conditional symmetry
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