On non-linear partial differential equations with an infinite-dimensional conditional symmetry

2004/02/29 by Roman Cherniha, Malte Henkel · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Geometry and complex manifolds #Nonlinear Waves and Solitons #cond-mat.stat-mech #hep-th #math-ph #math.AP #math.MP

paper · pdf · doi:10.1016/j.jmaa.2004.05.038

published as J. Math. Anal. Appl. 298, 487-500 (2004) · Latex2e, 14 pages, no figures; final form

openalex publication_date 2004/09/14 · arxiv created 2004/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 A₁(2) was introduced in J. Stat. Phys. \bf 75, 1023 (1994) and contains the Schrödinger Lie algebra sch₁ 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.

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• Galilean conformal algebras in two spatial dimension

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