Related papers: Motivic wave front sets
We discuss the mathematical aspects of wave field measurements used in traveltime inversion from seismograms. The primary information about the medium is assumed to be carried by the wave front set and its perturbation with repsect to a…
We find a novel phenomenon in the solution to the Wheeler-DeWitt equation by solving numerically the equation assuming $O(4)$-symmetry and imposing the Hartle-Hawking wave function as a boundary condition. In the slow-roll limit, as…
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am.…
The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck-Witt ring of the base field. Previous work of the first author and recent work of…
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\it Am.…
The immensely fruitful concept of Grothendieck topology or covering issued from the efforts of algebraic geometers to study "sheaf-like" objects defined on categories more general than the lattice of open sets on a topological space. In the…
In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper…
Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of wavefunction and wave equation for it.…
In the paper we develop the dressing method for the solution of the two-dimensional periodic Volterra system with a period N. We derive soliton solutions of arbitrary rank $k$ and give a full classification of rank 1 solutions. We have…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
The wave function in relativity is defined, in four-dimensional space, on a space-like three-dimensional plane. The plane, most close to the time-like region, is the light-front plane $ct+z=0$. Corresponding dynamical approach - the…
A formally exact discrete multi-resolution representation of quantum field theory on a light front is presented. The formulation uses an orthonormal basis of compactly supported wavelets to expand the fields restricted to a light front. The…
We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial…
We consider Scr\"odinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may be not even differentiable. The well-posedness of the Cauchy problem is proved in the frame of…
In this paper, we determine the wave front set of solutions to the Schr\"{o}dinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet…
Let G be a group SO(2n+1) defined over a p-adic field. We compute the wave front set of the anti-tempered irreducible representations of G(F) which are of unipotent reduction. It is the orthogonal orbit dual to the symplectic orbit…
In this paper we consider the Gabor wave front set of ultradistributions in the frame of ultradifferentiable functions. We prove that such a wave front set, defined through a Gabor frame on a regular lattice, is not affected by…
We introduce the Hamiltonian dynamics with the Hartree-Fock energy in new {\it wave-matrix} picture. Roughly speaking, the wave matrix is defined as the square root of the density matrix. The corresponding Hamiltonian equations are…
In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields, with high transverse localization, whose longitudinal…
Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics are taking place on a discrete half-space. All operators are represented graphically. The expressions…