We study a self-similar solution of the kinetic equation describing weak wave turbulence in
Bose–Einstein condensates. This solution presumably corresponds to an asymptotic …

We report numerical simulations of surface gravity waves forced at small scale and the
subsequent inverse cascade of wave action. We combine the spectral approach to …

In this paper, we study numerically the temporal evolution of an initially random large-scale
velocity field governed by the hyperviscous incompressible Navier-Stoke equations. Three …

Differential models for hydrodynamic, passive-scalar and wave turbulence given by
nonlinear first-and second-order evolution equations for the energy spectrum in the k-space …

We study a nonlinear equation which is equivalent to an equation of generalization of the
Leith model of turbulence and to the equation of the model of nonlinear diffusion in an …

We study Leith's model of turbulence represented by a nonlinear degenerate diffusion
equation (Leith 1967 Phys. Fluids 10 1409–16, Connaughton and Nazarenko 2004 Phys …

We study self-similar solutions of the kinetic equation for MHD wave turbulence derived in
(Galtier S et al 2000 J. Plasma Phys. 63 447–88). Motivated by finding the asymptotic …

Strong numerical hints exist in favor of a universal blowup scenario in the Sabra shell model,
perhaps the most popular cascade models of 3D turbulence, which features complex …

In this paper, we extend the classical Lie symmetry analysis from partial differential
equations to integro-differential equations with functional derivatives. We continue the work …

We study the model, describing a nonlinear diffusion process (or a heat propagation
process) in an inhomogeneous medium with non-stationary absorption (or source). We …