Related papers: The Radial Wave Operator in Similarity Coordinates
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
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.
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
In this paper we are consider radiating solitary wave solutions of coupled regularised Boussinesq equations. This type of solution consists of a leading solitary wave with a small-amplitude co-propagating oscillatory tail, and emerges from…
We study the inverse problem of recovery a compactly supported non-linearity in the semilinear wave equation $u_{tt}-\Delta u+ \alpha(x) |u|^2u=0$, in two and three dimensions. We probe the medium with complex-valued harmonic waves of…
In this work we give a few explicit formulas regarding the radiation fields of linear free waves. We then apply these formulas on the channel of energy theory. We characterize all the radial weakly non-radiative solutions in all dimensions…
Nonlinear water waves interacting with quasi-one-dimensional, non-uniformly periodic bed profiles are studied numerically in the deep-water regime with the help of approximate equations for envelopes of the forward and backward waves.…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
We analyze the wave equation in families of pp-wave geometries developing strong localized scale-invariant singularities in certain limits. For both cases of well-localized pp-waves and the so-called null-cosmologies, we observe an…
In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well known smooth and positive solitary wave with large wave speed,…
The radiation of harmonics during the interaction of nonrelativistic electrons with a powerful standing laser wave is studied. Expressions for the harmonic frequencies and the corresponding intensities of the spontaneous radiation are…
The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fields of free waves in the energy sub-critical case. We also…
We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the…
Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be…