Generating a New Higher-Dimensional Coupled Integrable Dispersionless System:Algebraic Structures,Bcklund Transformation and Hidden Structural Symmetries

摘要

The prolongation structure methodologies of Wahlquist-Estabrook [H.D.Wahlquist and F.B.Estabrook,J.Math.Phys.16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system.Based on the obtained prolongation structure,a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed.A Lie-Algebra representation of some hidden structural symmetries of the previous system,its Bcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived.In the wake of the previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation,which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.