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.

9 pages

References in corpus (2)

• Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions
• The Prolongation Problem for the Heavenly Equation

Cited by in corpus (6)

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• Algebraic structures generating reaction-diffusion models: the activator-substrate system
• Towers with skeletons for the (2+1)-dimensional continuous isotropic Heisenberg spin model