The integrable KP-I equation admits a nontrivial wave kinetic equation that thermalizes to generalized Rayleigh-Jeans equilibria via nonlocal spectral transfers, despite integrability.
One-dimensional optical wave turbulence: experiment and theory.Physics Reports, 514(4):121–175, 2012
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Wave Kinetics and Thermalization in Kadomtsev-Petviashvili-I System
The integrable KP-I equation admits a nontrivial wave kinetic equation that thermalizes to generalized Rayleigh-Jeans equilibria via nonlocal spectral transfers, despite integrability.