Related papers: Wave breaking in the short-pulse equation
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
New conditions for wave-wave interaction are considered. It is shown that using these conditions allows us to discover and describe new features of wave-wave interaction. Specifically, it is shown that an electromagnetic wave in a…
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…
We show that wave breaking occurs for the modified Camassa-Holm (mCH) equation. Next we classify all traveling wave solutions of the modified Camassa-Holm equation in the weak sense via parametrization of their maxima, minima and wave…
This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations…
If supersymmetry turns out to be a symmetry of nature at low energies, the first order of business to measure the soft breaking parameters. But one will also want to understand the symmetry, and its breaking, more microscopically. Two…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is…
We consider the scattering of linear waves in two dimensions by a rectangular region at the junction of four waveguides. A solution to the frequency domain problem is obtained by exploiting reflective symmetry to reduce the full problem to…
Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear…
We consider the initial boundary value problem in exterior domain for semilinear wave equations with power-type nonlinearity |u| p. We will establish blow-up results when p is less than or equal to Strauss' exponent which is the same one…
From a scale analysis of hydrodynamic phenomena having a significant action on the drift of an object in coastal ocean waters, we deduce equations modeling the associated hydrodynamic fields over a time period of several weeks. These models…
In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…
We consider quasilinear generalizations of the Korteweg-de Vries equation and dispersive perturbations of the Euler equations for compressible fluids, either in Lagrangian or in Eulerian coordinates. In particular, our framework includes…
We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length…
In this paper, we are focusing on proofs of a blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of a classical solution if the 0th moment of the initial…
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schr\"odinger equation. The present paper contains an existence…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We propose a simple way to determine the periodicities of wave packets in quantum systems directly from the energy differences of the states involved. The resulting classical periods and revival times are more accurate than those obtained…