Related papers: Generalized Maass Wave Forms
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
In this paper I introduce modular symbols for Maass wave cusp forms. They appear in the guise of finitely additive functions on the Boolean algebra generated by intervals with non--positive rational ends, with values in analytic functions…
We prove that Cohen's Maass wave form and Li-Ngo-Rhoades' Maass wave form are Hecke eigenforms with respect to certain Hecke operators. As a corollary, we find new identities of the $p$th coefficients of these Maass wave forms in terms of…
A general type of localized excitations, folded solitary waves and foldons, are defined and studied both analytically and graphically. The folded solitary waves and foldons may be "folded" in quite complicated ways and possess quite rich…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we…
Waves play an essential role in many aspects of plasma science, such as plasma manipulation and diagnostics. Due to the complexity of the governing equations, approximate models are often necessary to describe wave dynamics. In this…
We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of…
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain…
A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and…
Despite the tremendous success of general relativity so far, modified theories of gravity have received increased attention lately, motivated from both theoretical and observational aspects. Gravitational wave observations opened new…
This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New…
Bayesian inference of gravitational wave signals is subject to systematic error due to modelling uncertainty in waveform signal models, coined approximants. A growing collection of approximants are available which use different approaches…
In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a…
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in the study of the wave equation.