The Propagation of the Waves in Periodic Media at Large Time
نویسنده
چکیده
Asymptotics at large time of the Green function to the wave equation with periodic coefficients are found. A particular attention is given to its asymptotics near the wave front. It is shown that the spectral band (with number n = 0, 1, 2, ..) of the corresponding Hill operator is associated with a wave having the front velocity cn < 1. Estimates for cn in the terms of the gap lengths, the effective masses of the Hill operator are proved (both with fixed number n and their sums). Some extensions for more general cases ( the Dirac operator with periodic coefficients, the Schrodinger operator with finite band potentials etc.) are also obtained.
منابع مشابه
The Deterministic Generation of Extreme Surface Water Waves Based on Soliton on Finite Background in Laboratory
This paper aims to describe a deterministic generation of extreme waves in a typical towing tank. Such a generation involves an input signal to be provided at the wave maker in such a way that at a certain position in the wave tank, say at a position of a tested object, a large amplitude wave emerges. For the purpose, we consider a model called a spatial-NLS describing the spatial propagation o...
متن کاملInfluence of Rigidity, Irregularity and Initial Stress on Shear Waves Propagation in Multilayered Media
The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...
متن کاملPropagation of Waves at an Interface of Heat Conducting Elastic Solid and Micropolar Fluid Media
The present investigation is concerned with the reflection and transmission coefficients of plane waves at the interface of generalized thermoelastic solid half space and heat conducting micropolar fluid half- space. The amplitude ratios of various reflected and transmitted waves with various angle of incidence have been computed numerically and depicted graphically. Micropolarity and thermal r...
متن کاملWave Propagation in Fibre-Reinforced Transversely Isotropic Thermoelastic Media with Initial Stress at the Boundary Surface
The reflection and transmission of thermoelastic plane waves at an imperfect boundary of two dissimilar fibre-reinforced transversely isotropic thermoelastic solid half-spaces under hydrostatic initial stress has been investigated. The appropriate boundary conditions are applied at the interface to obtain the reflection and transmission coefficients of various reflected and transmitted waves wi...
متن کاملSteep. Short-Crested Waves and Related Phenomena
Steep, short-crested waves, as well as a large variety of three-dimensional propagating wave patterns have been created in laboratory, utilizing a plunging half-cone. Monochromatic waves, over a range of frequencies and amplitudes through breaking and including soliton wave groups near resonance, have been observed and studied in a small wave flume. This monochromatic wavemaker creates complex ...
متن کاملکاربرد روش معادله سهموی در تحلیل مسائل انتشار امواج داخل ساختمان
With the rapid growth of indoor wireless communication systems, the need to accurately model radio wave propagation inside the building environments has increased. Many site-specific methods have been proposed for modeling indoor radio channels. Among these methods, the ray tracing algorithm and the finite-difference time domain (FDTD) method are the most popular ones. The ray tracing approach ...
متن کامل