Turbulence in Integrable Systems

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Integrable turbulence and formation of rogue waves (2014, background): “First, we expect that after a very long evolution the result of the MI should be the stationary ”integrable turbulence” [1] - thermodynamically equilibrium state defined by infinite number of invariants.”
Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics (2014, methodology): “This is consistent with the fact that when one applies the conventional WT procedure to the integrable NLS equation, one obtains that all collision terms in the kinetic equation vanish identically at any order [390].”
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, background): “Whether and how the results on the infinite line reduce to those with periodic boundary conditions as the characteristic width of the perturbations increases without bounds, and the understanding of the precise connections between the phenomena discussed in this work and the theory of integrable tur”