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We construct solitary wave solutions in a $1+1$ dimensional massless scalar ($\phi$) field theory with a specially chosen potential $V(\phi)$. The equation governing perturbations about this solitary wave has an effective potential which is…
The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known iterative formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for…
We present a composite optical cavity made of standard laser mirrors; the cavity consists of a suitable combination of stable and unstable cavities. In spite of its very open nature the composite cavity shows ray chaos, which may be either…
Recent detections of gravitational waves have made black hole quasinormal modes a powerful tool in testing predictions of general relativity. Understanding the spectrum of these quasinormal modes in a broad class of theories beyond general…
In this brief note we give a brief overview of the comprehensive theory, recently obtained by the author jointly with Johnson, Noble and Zumbrun, that describes the nonlinear dynamics about spectrally stable periodic waves of parabolic…
A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a periodic standing wave state above onset…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
It has been shown, via specific examples and a pseudospectrum analysis, that the black hole quasinormal spectra are unstable. The implication of such a result for gravitational-wave physics and of our understanding of black holes is, still,…
We consider an array of coupled optical cavities, each containing a multi-atom ensemble. We show that the nonlinearity inherent in the cooperative dynamics of the atoms in each ensemble coupled to the respective cavity field allows for the…
Based on the representation theory of the $q$-deformed Lorentz and Poincar\'e symmeties $q$-deformed relativistic wave equation are constructed. The most important cases of the Dirac-, Proca-, Rarita-Schwinger- and Maxwell- equations are…
This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes…
We study the long-time behavior of the Schr{\"o}dinger flow in a heterogeneous potential $\lambda$V with small intensity 0<$\lambda$$\ll$1 (or alternatively at high frequencies). The main new ingredient, which we introduce in the general…
In recent work, Baird et al. have introduced a generalized Maslov index which allows oscillation techniques that have previously been restricted to eigenvalue problems with underlying Hamiltonian structure to be extended to the…
Light emission from a dielectric cavity with a stadium shape is studied in both ray and wave models. For a passive cavity mode with low loss, a remarkable correspondence is found between the phase space representation of a quasi-bound…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
We present Vlasov-Poisson 3-D linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel…
Parametric Instability (PI) is a phenomenon that results from resonant interactions between optical and acoustic modes of a laser cavity. This is problematic in gravitational wave interferometers where the high intra-cavity power and low…
Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic…