Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
Accueil
Accès
Personnel
Publications
Articles dans des revues à comité de lecture
Lettres
Actes de conférences invités
Actes de conférences
Non publié
Thèse
Habilitation à diriger des recherches
Epistémologie, histoire des sciences
Articles à vocation pédagogique
Livres
Edition d'ouvrage
Chapitres de livre
Vulgarisation
Séminaires
Ateliers
Rencontres
Ecoles
International
Grp Travail
Theses, Postes
Enseignement

Articles dans des revues à comité de lecture

On non-linear partial differential equations with an infinite-dimensional conditional symmetry
Cherniha R., Henkel M.
Journal of Mathematical Analysis and Applications 298 (2004) 487
DOI : 10.1016/j.jmaa.2004.05.038
ArXiv : math-ph/0402059 [PDF]

The invariance of non-linear partial differential equations under a certain infinite-dimensional Lie algebra UN (z) in N spatial dimensions is studied. The special case U1 (2) was introduced in [J. Stat. Phys. 75 (1994) 1023] and contains the Schroedinger 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 UN (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 UN (z) such that the well-known Monge-AmpeÌEURre equation is the required additional condition. New exact solutions are found for some representatives of this class.



Haut de page