Related papers: Chirped Elliptic Waves: Coupled Helmholtz Equation…
Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
The container motion along a planar circular trajectory at a constant angular velocity, i.e. orbital shaking, is of interest in several industrial applications, e.g. for fermentation processes or in cultivation of stem cells, where good…
We show that the non-relativistic theory of mutual coherence and localization in Coulomb-disordered media can be extended to relativistic electron beams used in transmission electron microscopy (TEM). Starting from the Dirac equation, we…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…
We study the existence and stability of the standing waves for the periodic cubic nonlinear Schr\"odinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
The Warm Plasma Dispersion Relation, for waves in the electron cyclotron resonance range of frequencies, can be cast into the form of a bi-quadratic equation for $N_\perp$, where the coefficients are a function of $N_\perp^2$ and an…
Nonlinear wave--coupling is studied in a multi-species degenerate astrophysical plasma consisting of two electron species (at different temperatures): a highly degenerate main component plus a smaller classical relativistic flow immersed in…
We propose a new method to measure parameters of SMBHBs as individual resolvable evolving single GWs sources, using the timing data of three or more non-simultaneous pulsars. These parameters include the sky position of the SMBHB and a…
The main purpose of this paper is to capture the asymptotic behavior for solutions to a class of nonlinear elliptic and parabolic equations with the anisotropic weights consisting of two power-type weights of different dimensions near the…
We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a…
Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…
Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term…
The problem of a test body in the Schwarzschild geometry is investigated in a Keplerian limit. Beginning with the Schwarzschild metric, a solution to the limited case of approximately elliptical (Keplerian) motion is derived in terms of…
We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one…
We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed…