Related papers: Decay of the monochromatic capillary wave
We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main…
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…
We study theoretically the capillary-gravity waves created at the water-air interface by a small object during a sudden accelerated or decelerated rectilinear motion. We analyze the wave resistance corresponding to the transient wave…
We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.
We describe an experimental test of whether particle decay causes wave function collapse. The test uses interference between two well separated, but coherent, sources of vector mesons. The short-lived mesons decay before their wave…
On the basis of general theoretical results developed previously in [I. M. Sokolov et al., J. Exp. Theor. Phys. 112, 246 (2011)], we analyze spontaneous decay of a single atom inside cold atomic clouds under conditions when the averaged…
The propagation of water waves is altered when interacting with curved surfaces. Here, we consider the problem of capillary waves interacting with a 3D meniscus. We show that when capillary waves scatter off an object surrounded by a…
Elastic scattering governed by the Lame system associated with the third-type or fourth-type boundary condition is considered. It was shown in [8] by two of the authors that under suitable geometric conditions on the boundary surface of the…
In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on…
The decoherence of two qubits, coupled with one-mode cavity separately, has been investigated exactly. The results show that, for the resonant case, the decoherence behavior of system is similar to Markovian case when the coupling strength…
Cold atomic clouds constitute highly resonant nonlinear optical media, whose refractive index can be easily tuned via the light frequency. When subjected to a retro-reflected laser beam and under appropriate conditions, the cloud undergoes…
Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The…
Traditionally resonant interactions among short waves, with large real wave-numbers, were described statistically and only a small domain in spectral space with integer wave-numbers, discrete resonances, had to be studied separately in…
The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
The basic ideas of a homotopy-based multiple-variable method is proposed and applied to investigate the nonlinear interactions of periodic traveling waves. Mathematically, this method does not depend upon any small physical parameters at…
In this article we exploite the uniform decay for damped linear wave equation with Zaremba boundary condition, obtained in a previous work, to treat the same problem in nonlinear context. We need a uniqueness assumption, usual for this type…
The extraordinary properties of resonant four-wave mixing of backward waves in doped negative-index materials are investigated. The feasibility of independent engineering of negative refractive index and nonlinear optical response as well…
In this paper, we study the nonlinear stability of the composite wave consisting of planar rarefaction and planar contact waves for viscous conservation laws with degenerate flux under multi-dimensional periodic perturbations. To the level…
Observations of coronal waves (CWs) interacting with coronal holes (CHs) show the formation of typical wave-like features, such as reflected, refracted and transmitted waves (collectively, secondary waves). In accordance with these…