Related papers: The wave front set of oscillatory integrals with i…
Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where…
The recently developed concept of refracting profiles and that of refraction holodiagrams are combined so that the classical Abramson holodiagrams can be generalized taking into account a wider class of wave fronts and refraction at an…
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of…
In this paper we develop a new statistical model for the irradiance fluctuations of an unbounded optical wavefront (plane and spherical waves) propagating through a turbulent medium under all irradiance fluctuation conditions in…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
Dissipative quantum systems are sometimes phenomenologically described in terms of a non-hermitian hamiltonian $H$, with different left and right eigenvectors forming a bi-orthogonal basis. It is shown that the dynamics of waves in open…
The new mechanism for obtaining a nonlinear phase shift has been proposed and the schemes are described for its implementation. As it is shown, the interference of two waves with intensity-dependent amplitude ratio coming from the second…
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
A different approach has been used to evaluate the momentum imparted by the gravitational waves with spherical wavefronts. It is shown that the results obtained for momentum coincide with those already available in the literature.
Conditions on the elastic stiffnesses of anisotropic crystals are derived such that circularly polarized longitudinal inhomogeneous plane waves with an isotropic slowness bivector may propagate for any given direction of the normal to the…
A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude…
In the framework of decay theory of Goldberger and Watson we treat $\alpha$-decay of nuclei as a transition caused by a residual interaction between the initial unperturbed bound state and the scattering states with alpha-particle. The…
We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase.…
A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
It is well known that the classical and Sobolev wave fronts were extended into non-equivalent global versions by the use of the short-time Fourier transform. In this very short paper we give complete characterisations of initial wave front…
The generalized invariant and its eigenstates of a general quadratic oscillator are found. The Schr\"odinger wave functions for the eigenstates are also found in analytically closed forms. The conditions for the existence of the cyclic…
We predict high-order harmonics in which the polarization within the spectral bandwidth of each harmonic varies continuously and significantly. For example, the interaction of counter-rotating circularly-polarized bichromatic drivers having…
Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…