Related papers: Generalized Maass Wave Forms
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We develop a formalism, based on spinor-helicity techniques, to generalize the formulation of partial wave unitarity bounds. We discuss unitarity bounds for $N \to M$ (with $N,M \geq 2$) scattering processes -- relevant for high-energy…
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
The multivariate analogue of Dalamber's equation in the space of generalized functions is considered. The method of generalized functions for the building of solutions of nonstationary boundary value problems for wave equations in spaces of…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
This Chapter outlines the basic properties of waves in solar partially ionized plasmas. It provides a summary of the main sets of equations, from the single-fluid formalism, to the multi-fluid one, giving examples for purely hydrogen, and…
The propagation of a gravitational wave (GW) through a magnetized plasma is considered. In particular, we study the excitation of fast magnetosonic waves (MSW) by a gravitational wave, using the linearized general-relativistic hydromagnetic…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly- Euler polynomials. Moreover, we introduce a more general form of multi…
Gravitational wave echoes may imply physics beyond general relativity; however, several approaches to searching for echoes require fitting the data to toy templates which are not physically motivated. Here, I create a procedure which…
The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…
It is well known that the Gaussian wave packet dynamics can be written in terms of Hamilton equations in the extended phase space that is twice as large as in the corresponding classical system. We construct several generalizations of this…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
Looking at rational solid-fluid mixture theories in the context of their biomechanical perspectives, this work aims at proposing a two-scale constitutive theory of a poroelastic solid infused with an inviscid compressible fluid. The…
In this paper, we introduce the notion of generalized $s$-manifolds, which is a generalization of symmetric spaces. Then we give a method to construct generalized $s$-manifolds and present some typical examples. We study polars and…
The fields in rectangular and circular waveguides are derived from Maxwell's equations by superposition of plane waves. Subsequently the results are applied to explain cavity modes. Interaction of the cavity modes with a charged particle…