Generating a New Higher-Dimensional Ultra-Short Pulse System: Lie-Algebra Valued Connection and Hidden Structural Symmetries

We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media. Based upon the Wahlquist-Estabrook approach, we construct the Lie-algebra valued connections associated to the previous symmetries while deriving their corresponding Lax-pairs, which are particularly useful in soliton theory. In the wake of previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional ultra-short pulse equation is unveiled along with its inverse scattering formulation, the application of which are straightforward in nonlinear optics where an additional propagating dimension deserves some attention.