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.