In the subcritical ν→0 then L→∞ limit, exact NLS spectra satisfy the wave kinetic equation up to O(ε^3), proved by cumulant induction instead of Feynman diagrams.
An algebraic geometry question and wave turbulence
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This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
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Kinetic approximation for equations of discrete turbulence in the subcritical case
In the subcritical ν→0 then L→∞ limit, exact NLS spectra satisfy the wave kinetic equation up to O(ε^3), proved by cumulant induction instead of Feynman diagrams.