10 citations · 22 across the 7 of their papers we have counts for
7 papers
Explicit form of the effective evolution equation for the randomly forced Schrödinger equation with quadratic nonlinearity
Huilin Zhang, Elena Tobisch
An effective equation describes a weakly nonlinear wave field evolution governed by nonlinear dispersive PDEs \emph{via} the set of its resonances in an arbitrary big but finite do…
Direct dynamical energy cascade in the modified KdV equation
Denys Dutykh, Elena Tobisch
In this study we examine the energy transfer mechanism during the nonlinear stage of the Modulational Instability (MI) in the modified Korteweg-de Vries equation. The particularity…
Single evolution equation describing nonlinear dynamics of nonlocal optical medium under two-wave mixing
Svitlana Bugaychuk, Elena Tobisch
In this Letter we study theoretically the interaction of optical waves in nonlinear dynamical medium, i.e. medium with relaxation. Taking into account the relaxation of the photoin…
Resonance enhancement by suitably chosen frequency detuning
Denys Dutykh, Elena Tobisch
In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation…
What can go wrong when applying wave turbulence theory
Elena Tobisch
Many new models of wave turbulence -- frozen, mesoscopic, laminated, decaying, sand-pile, etc. -- have been developed in the last decade aiming to solve problems seemingly not solv…
Energy spectrum of ensemble of weakly nonlinear gravity-capillary waves on a fluid surface
Elena Tobisch
In this Letter we regard nonlinear gravity-capillary waves with parameter of nonlinearity being . For this nonlinearity time scale separation does not o…
Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation
Denys Dutykh, Elena Tobisch
In this Letter we demonstrate for the first time the formation of the inverse energy cascade in the focusing modified Korteweg-de Vries (mKdV) equation. We study numerically the pr…