The integrable KP-I equation admits a nontrivial wave kinetic equation that thermalizes to generalized Rayleigh-Jeans equilibria via nonlocal spectral transfers, despite integrability.
Wave turbulence in integrable systems: nonlinear propagation of incoherent optical waves in single-mode fibers.Optics express, 19(18):17852–17863, 2011
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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.