Turbulent cascades in a truncation of the cubic Szegő equation and related systems

The cubic Szego equation has been studied as an integrable model for deterministic turbulence, starting with the foundational work of Gerard and Grellier. We introduce a truncated version this equation, wherein majority Fourier mode couplings are eliminated while signature features preserved, namely, Lax-pair structure nested hierarchy finite-dimensional dynamically invariant manifolds. Despite impoverished interactions, turbulent behaviors our new stronger in appropriate sense than original equation. construct explicit analytic solutions displaying exponential growth Sobolev norms. furthermore family models that interpolate between system along few other related deformations. All these possess Lax pairs, manifolds, display variety cascades. additionally mention numerical evidence shows even type turbulence form finite-time blow-up some different, closely dynamical systems.