Related papers: Inhomogeneous Travelling-Wave Accelerating Section…
We consider the quartic focusing Half Wave equation (HW) in one space dimension. We show first that that there exist traveling wave solutions with arbitrary small $H^{\frac 12}(\R)$ norm. This fact shows that small data scattering is not…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
A general equation describing the resonant nonlinear mode-coupling among kinetic Alfv\'en waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As…
Attosecond streaking, as a measurement technique, was originally conceived as a means to characterize attosecond light pulses, which is a good approximation if the relevant transition matrix elements are approximately constant within the…
The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by…
We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines a WKB treatment of the long range attraction with the Fraunhofer model treatment of the short…
Recent advances in the field of structured waves have resulted in sophisticated coherent wavefront shaping schemes that provide unprecedented control of waves in various complex settings. These techniques exploit multiple scattering events…
Traveling wave parametric amplifiers (TWPAs) have recently emerged as essential tools for broadband near quantum-limited amplification. However, their use to generate microwave quantum states still misses an experimental demonstration. In…
Lenses that can collect the perfect image of an object must restore propagative and evanescent waves. However, for efficient information transfer, e.g., in compressed sensing, it is often desirable to detect only the fast spatial variations…
In this manuscript, we prove the existence of slow and fast traveling wave solutions in the original Gatenby--Gawlinski model. We prove the existence of a slow traveling wave solution with an interstitial gap. This interstitial gap has…
In Kohn-Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane-wave expansions give a poor approximation of the eigenfunctions. In conjunction with the use of…
This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…
Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…
In this work, we apply the factorization technique to the Benjamin-Bona-Mahony like equations, B(m,n), in order to get travelling wave solutions. We will focus on some special cases for which m is not equal to n, and we will obtain these…
Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components while the classic random sweeping…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
We consider interactions between surface and interfacial waves in the two layer system. Our approach is based on the Hamiltonian structure of the equations of motion, and includes the general procedure for diagonalization of the quadratic…
Wireless Body Area Networks (WBANs) have gained significant attention due to their applications in healthcare monitoring, sports, military communication, and remote patient care. These networks consist of wearable or implanted sensors that…
An original entity is defined to study quantum beams of conserved particles. The beam is described as a Stationary Incoherent Superposition of Wave packets (SISOW). Mean values are time-independent confirming that the SISOW describes a…
Internal waves in the ocean interact in triads. Early work emphasized the importance of extreme-scale separated interactions in which two large wavenumber waves interact with one small wavenumber wave. More recent efforts have called this…