Related papers: Quasi-paraxial theory for coupled unstable cavitie…
In a two-dimensional microwave chaotic cavity ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous…
Paraxial propagation of a quasi-monochromatic light wave with two circular polarizations in a defocusing Kerr medium with anomalous dispersion inside a waveguide of annular cross-section was considered. In the phase-separated mode, the…
We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber…
We consider a random wave model introduced by Zelditch to study the behavior of typical quasi-modes on a Riemannian manifold. Using the exponential moment method, we show that random waves satisfy the quantum unique ergodicity property with…
It is known that the spectrum of quasi-normal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasi-normal modes, but it…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…
We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations…
The one-quasihole wavefunctions and their norms are derived for the system of particles on the line with inverse-square interactions and harmonic confining potential.
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
This paper concerns the interaction between non-axisymmetric inertial waves and their corotation resonances in a hydrodynamical disk. Inertial waves are of interest because they can localise in resonant cavities circumscribed by Lindblad…
Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave…
We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The…
We investigate the conditions for the emergence of wave instabilities in a vacuum cavity delimited by cylindrical metallic walls under rotation. It is shown that for a small vacuum gap and for an angular velocity exceeding a certain…
Backward waves and negative refraction are shown to exist in plasmonic crystals whose lattice cell size is a very small fraction of the vacuum wavelength (less than 1/40th in an illustrative example). Such ``quasi-homogeneity'' is…
We clarify the purely imaginary quasinormal frequencies of a massless scalar perturbation on the 3D charged-dilaton black holes. This case is quite interesting because the potential-step appears outside the event horizon similar to the case…
Using the method of separation of variables, we developed a vector nonparaxial theory from the nonlinear wave equations in strong field approximation of a Kerr media. Investigating three waves on different frequencies, which satisfied the…
This study proposes a novel coupled-mode theory for two-dimensional exterior Helmholtz problems. The proposed approach is based on the separation of the entire space R2 into a fictitious disk and its exterior. The disk is allocated in such…
In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model…
Variational inequalities, formulated on unknown dependent convex sets, are called quasi-variational inequalities (QVI). This paper is concerned with the abstract approach to a class of parabolic QVIs arising in many biochemical/mechanical…