Nonlinear 2+1--Dimensional Field Equations from Incomplete Lie Algebra Structures
Abstract
We show that the nonlinear 2+1--dimensional Three--Wave Resonant Interaction equations, describing several important physical phenomena, can be generated starting from incomplete Lie algebras in the framework of multidimensional prolongation structures. We make use of an {\em ansatz} involving the structure equations of a principal prolongation connection induced by an admissible Bäcklund map.