SKIPP , Jonathan

Abstract We study the thermodynamic equilibrium spectra of the Charney–Hasegawa–Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross–Pitaevskii equations, which are examples for comparison. We explore how the third invariant...

Abstract We study the thermodynamic equilibrium spectra of the Charney–Hasegawa–Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross–Pitaevskii equations, which are examples for comparison. We explore how the third invariant...

Abstract We study the thermodynamic equilibrium spectra of the Charney–Hasegawa–Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross–Pitaevskii equations, which are examples for comparison. We explore how the third invariant...

The statistical evolution of ensembles of random, weakly-interacting waves is governed by wave kinetic equations. To simplify the analysis, one frequently works with reduced differential models of the wave kinetics. However, the conditions for deriving such reduced models are seldom justified self-consistently. Here, we derive a reduced model...

We present a rigorous derivation of the point vortex model from the two-dimensional nonlinear Schrödinger equation, from the Hamiltonian perspective, in the limit of well-separated vortices on the background of a strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex for the...

We develop the theory of weak wave turbulence in systems described by the Schrödinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schrödinger equation, and the Schrödinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which...