Related papers: Pattern Formation with Two Length Scales: Spatiote…

In propagating wave systems, three or four-wave resonant interactions constitute a classical non-linear mechanism exchanging energy between the different scales. Here we investigate three-wave interactions for gravity-capillary surface…

Charge and spin density waves, periodic modulations of the electron and magnetization densities, respectively, are among the most abundant and non-trivial low-temperature ordered phases in condensed matter. The ordering direction is widely…

The step bunching instability is studied in three models of step motion defined in terms of ordinary differential equations (ODE). The source of instability in these models is step-step attraction, it is opposed by step-step repulsion and…

In this paper, we establish the existence and instability of standing wave for a system of nonlinear Schr\"{o}dinger equations arising in the two-wave model with quadratic interaction in higher space dimensions under mass resonance…

We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by a sine wave. The calculation is simple…

This thesis presents a newly developed theory for the formation and maintenance of eddy-driven jets in planetary turbulence. The novelty is that jet formation and maintenance is studied as a dynamics of the statistics of the flow rather…

Generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated traps is investigated. The generation of waves is achieved by periodically changing a parameter of the system in time. Two types of modulations of parameters are…

We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the…

We study bright solitary waves of three dimensional trapped Bose-Einstein condensates and their collisions. For a single solitary wave, in addition to an upper critical number, we also find a {\em lower} cut-off, below which no stable state…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

Temporal periodic modulation of the interatomic s-wave scattering length in Bose-Einstein condensates is shown to excite subharmonic patterns of atom density through a parametric resonance. The dominating wavelength of the spatial…

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying sub-wavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern…

We study the quantum evolution in dimension three of a system composed by a test particle interacting with an environment made of $N$ harmonic oscillators. At time zero the test particle is described by a spherical wave, i.e. a highly…

Planetary turbulence is observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models that retains the relevant dynamics of turbulent self-organization is a barotropic flow in a…

In the following we consider a 2-dimensional system of ODE's containing quasiperiodic terms. The system is proposed as an extension of Mathieu-type equations to higher dimensions, with emphasis on how resonance between the internal…

We consider a diatomic chain characterized by a cubic anharmonic potential. After diagonalizing the harmonic case, we study in the new canonical variables, the nonlinear interactions between the acoustical and optical branches of the…

We use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad…

Holmboe (1962) postulated that resonant interaction between two or more progressive, linear interfacial waves produces exponentially growing instabilities in idealized (broken-line profiles), homogeneous or density stratified, inviscid…

We consider a family of spin-1/2 models with few-body, SU(2) invariant Hamiltonians and analytical ground states related to the 1D Haldane-Shastry wavefunction. The spins are placed on the surface of a cylinder, and the standard 1D…

The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations…