A detailed study of the Charney–Hasegawa–Mima model and its extensions is presented.
These simple nonlinear partial differential equations suggested for both Rossby waves in …

Nonlinear resonance analysis is a unique mathematical tool that can be used to study
resonances in relation to, but independently of, any single area of application. This is the first …

Two fundamental facts of the modern wave turbulence theory are 1) existence of power
energy spectra in k-space, and 2) existence of “gaps” in this spectra corresponding to the …

In this letter we propose discrete wave turbulence (DWT) as a counterpart of classical
statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the …

A robust energy transfer mechanism is found in nonlinear wave systems, which favors
transfers toward modes interacting via triads with nonzero frequency mismatch, applicable in …

In this letter we show how the nonlinear evolution of a resonant triad depends on the special
combination of the modes' phases chosen according to the resonance conditions. This …

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave
equation. A cluster consists of N modes forming a total of M connected triads. We investigate …

We consider the set of Diophantine equations that arise in the context of the partial
differential equation called “barotropic vorticity equation” on periodic domains, when …

We investigate an effect of the resonant interaction in the case of one-directional
propagation of capillary-gravity surface waves arising as the free surface of a rotational …

We revisit the problem of a triad of resonantly interacting nonlinear waves driven by an
external force applied to the unstable mode of the triad. The equations are Hamiltonian, and …