A dynamically consistent model of a meandering jet stream with two Rossby waves obtained using the law conservation potential vorticity is investigated. Stationary points are found in phase space advection equations and type their stability determined analytically. All topologically different flow regimes bifurcations for stationary (taking into account only first wave). The results can be used...

A mathematical framework is presented to study the evolution of multi-point cumulants in nonlinear dispersive partial differential equations with random input data, based on the theory of weak wave turbulence (WWT). This framework is used to explain how energy is distributed among Fourier modes in the nonlinear Schrödinger equation. This is achieved by considering interactions among four Fourie...

For the stationary one-dimensional nonlinear Schrödinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi–) analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a single quantum well (respectively a double barri...

We develop a theory of particle acceleration inside relativistic rotating electron-positron force–free jets with spiral magnetic fields. We considered perturbation of the stationary magnetic field structure and found that acceleration takes place in the regions where the Alfvén resonant condition with the eigenmodes in the jet is fulfilled, i.e. where the local Alfvén speed is equal to the phas...

We study theoretically the quantum dynamics of an electron in the symmetric four-level double-dot structure under the influence of the monochromatic resonant pulse. The probability amplitudes of the eigenstates relevant for the quantum dynamics are found from the solution of the non-stationary Schrödinger equation. The first-order correction term to the solution obtained through the rotating wa...

Quantum optical systems, like trapped ions, are routinely described by master equations. The purpose of this paper is to introduce a master equation for two-sided optical cavities with spontaneous photon emission. To do so, we use the same notion of photons as in linear optics scattering theory and consider a continuum of travelling-wave cavity photon modes. Our model predicts the same stationa...

A variety of stationary and wave patterns that show a complicated spatial structure but are ordered in the Fourier space can be constructed by considering interaction of noncollinear modes near a symmetry breaking bifurcation point. The planform selection is particularly rich in the presence of resonant (phase-dependent) interactions among degenerate modes. We consider the problem of pattern se...

We establish the equation of motion of pseudoscalar particles coupled to an electromagnetic field in a classical gravitational background through the use of conformal time and flat geometry. We show that the expansion of the universe can lead to larger mixing than in a stationary universe. We also show that for a broad range of parameters, one can obtain resonant mixing, i.e. a region in which ...

The photorefractive properties of semi-insulating AlGaAs-GaAs multiple quantum wells are described for the transverse Franz-Keldysh geometry with the electric field in the plane of the quantum wells. Combining the strong electroabsorption of quantum-confined excitons with the high resistivity of semi-insulating quantum wells yields large nonlinear optical sensitivities. The photorefractive quan...

We theoretically investigate resonant tunneling through a linear array of quantum dots with subsequent tunnel coupling. We consider two limiting cases: ~i! the strong Coulomb blockade, where only one extra electron can be present in the array; ~ii! the limit of almost noninteracting electrons. We develop a densitymatrix description that incorporates the coupling of the dots to reservoirs. We an...