共查询到20条相似文献,搜索用时 125 毫秒
1.
N. N. Rozanov 《Optics and Spectroscopy》2008,104(2):248-252
The generation of counterpropagating waves with low frequencies by pump copropagating waves in a weakly nonlinear medium is analyzed. The generation is shown to be efficient in the presence of intervals with anomalous and normal dispersion in the spectrum. Under these conditions, the approximation of unidirectional propagation, which is widely used in the literature, is incorrect and the nonlinear propagation of radiation should be described by the full wave equation. 相似文献
2.
根据Mindlin理论,考虑宏观尺度非线性效应、二次和三次微尺度非线性效应以及微尺度频散效应,建立了描述一维微结构固体中纵波传播的一种新模型.用动力系统定性分析理论,分析了微结构固体中孤立波的存在条件及其几何特征,证明了当介质参数和孤立波传播速度满足适当条件时,在二次微尺度非线性效应的影响下微结构固体中可以形成一种非对称孤立波,在三次微尺度非线性效应的影响下微结构固体中可以形成一种对称孤立波.最后,用数值方法进一步验证了上述结论. 相似文献
3.
K. Yu. Bulgakov 《Physics of Wave Phenomena》2017,25(1):78-82
The shallow-water propagation of a nonlinear wave formed in deep water has been numerically analyzed based on the conformal model of surface waves. The lifetime of wave until its collapse is investigated. The parameters at which extreme waves may occur are found. An example of practical application of the simulation results is presented. 相似文献
4.
Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere
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Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations
with a higher-degree of nonlinear terms are derived from a simple
incompressible non-hydrostatic Boussinesq equation set in atmosphere
and are used to investigate gravity waves in atmosphere. By taking
advantage of the auxiliary nonlinear ordinary differential equation,
periodic wave and solitary wave solutions of the fifth-order
KdV--mKdV models with higher-degree nonlinear terms are obtained
under some constraint conditions. The analysis shows that the
propagation and the periodic structures of gravity waves depend on
the properties of the slope of line of constant phase and atmospheric
stability. The Jacobi elliptic function wave and solitary wave
solutions with slowly varying amplitude are transformed into
triangular waves with the abruptly varying amplitude and breaking
gravity waves under the effect of atmospheric instability. 相似文献
5.
G. A. Maugin 《The European physical journal. Special topics》2007,147(1):209-230
First a general introduction on the notion of surface waves on solids (types of different waves), a reminder on the simplest
familiar nonlinear dispersive model equations, and another on the basic equations of nonlinear elasticity are given. Then
attention is focused on the linear surface wave problem. The main properties of nonlinear surface waves in the absence of
dispersion are studied next by use of several asymptotic techniques. The additional effects of dispersion are then considered
and combined with those of nonlinearity with an emphasis on the case of so-called shear-horizontal surface waves and solitary-wave
solutions for envelope signals. Finally, typical nonlocality is introduced for nonlinear Rayleigh surface waves, and general
comments on more general two-dimensional (in propagation space) nonlinear strain waves on structures are evoked by way of
conclusion. 相似文献
6.
The results of theoretical investigation of propagation of electromagnetic wave pulses in nonlinear dielectric plates, taking into account the dispersion introduced by the plate to the maximum possible extent, are presented. The investigation is aimed at obtaining the shortest possible pulses of electromagnetic waves. Pulse compression is based on the collapse of electromagnetic waves in transparent dielectrics with electronic non-linearity. The integral equation for describing the pulse compression is derived, and conditions under which a pulse is compressed relative to time and one of the transverse coordinates are determined. Numerical simulation shows that quite short (on the order of a few femtoseconds) pulses can be obtained in this way. 相似文献
7.
A. V. Slunyaev 《Journal of Experimental and Theoretical Physics》2005,101(5):926-941
A third-order nonlinear envelope equation is derived for surface waves in finite-depth water by assuming small wave steepness, narrow-band spectrum, and small depth as compared to the modulation length. A generalized Dysthe equation is derived for waves in relatively deep water. In the shallow-water limit, one of the nonlinear dispersive terms vanishes. This limit case is compared with the envelope equation for waves described by the Korteweg-de Vries equation. The critical regime of vanishing nonlinearity in the classical nonlinear Schrödinger equation for water waves (when kh ≈ 1.363) is analyzed. It is shown that the modulational instability threshold shifts toward the shallow-water (long-wavelength) limit with increasing wave intensity. 相似文献
8.
Using the nonlinear dependence of sound propagation speed with pressure, we evidence the anomalous elastic softness of a granular packing in the vicinity of the jamming transition. Under gravity and close to a free surface, the acoustic propagation is only possible through surface modes guided by the stiffness gradient. These Rayleigh-Hertz modes are evidenced in a controlled laboratory experiment. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of nonlinear elasticity including finite size effects. These results allow one to access the elastic properties of the packing under vanishing confining pressure. 相似文献
9.
The formation of solitary elastic surface pulses from laser-generated pulselike initial conditions is reported. The nonlinearity of the medium is compensated by both normal dispersion and anomalous dispersion, which were realized by coating isotropic fused silica by a metal and titanium nitride film, respectively. As an anisotropic material, silicon covered with an oxide layer was studied. The experimental results agree with numerical simulations carried out with a nonlocal evolution equation, which describes nonlinear propagation of surface acoustic waves in a dispersive medium. 相似文献
10.
The experimental measurements of the propagation properties of self-exicted ion acoustic waves in a de-low pressure column are compared with a one dimensional dispersion theory. The corresponding dispersion relation is developed starting from the linearised Vlasov equation with a Davydov-type collision term. It is shown, that the mean features of the propagation behaviour of the ion acoustic waves can be explained by the theory. The experimental results concerning the dependence of the upper limit frequency of the waves upon the discharge current should be analysed on the base of new results from plasma diagnostics, taking also into account nonlinear and geometrical effects. 相似文献
11.
In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish. 相似文献
12.
Spatiotemporal self-similar waves of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation, describing propagation of optical pulses in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain, are derived. A one-to-one correspondence between such self-similar waves and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss dynamical behaviors of self-similar waves in dispersion decreasing fiber. 相似文献
13.
The possibility of new weakly nonlinear solitary waves in nonlocal elastic media is demonstrated. The properties of these waves are determined by the characteristic features of wave dispersion in the linear approximation, and their velocity and amplitude cannot exceed certain limiting values. In the case of small amplitudes and velocities close to the velocity of sound, the profile of the waves under consideration coincides with the profile of the soliton described by the Korteweg-de Vries equation. When the amplitude and velocity of the aforementioned waves reach their limiting values, the wave profile sharpens. It is concluded that the propagation of such waves in rocks and soils is possible. 相似文献
14.
15.
Paul S.N. Kashyapi P.K. Chakraborty B. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1992,20(5):481-486
The nonlinear dispersion relation for an electromagnetic wave propagating through a cold, homogeneous magnetized rotating plasma is derived to investigate certain nonlinear effect for the case where only the Coriolis force part of the consequences of rotation is taken into account. Characteristics of variation of refractive indices with variation of the wave amplitude and rotational frequency are discussed. It is shown that the nonlinear effects considerably influence the propagation of waves in rotating plasmas 相似文献
16.
17.
Nikolai A. Kudryashov Pavel N. RyabovDmitry I. Sinelshchikov 《Physics letters. A》2011,375(20):2051-2055
Nonlinear waves described of the fifth order dispersive nonlinear evolution equation are numerically investigated. The numerical method for boundary value problem for this equation is proposed. Exact solutions to nonlinear evolution equation of the fifth order are given. The numerical method was tested using some exact solutions. The influence of the fifth order dispersion on the propagation of nonlinear waves and formation of the periodic structures is studied. 相似文献
18.
A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones). 相似文献
19.
A.?G.?Kulikovski? A.?P.?Chuga?nova 《Journal of Experimental and Theoretical Physics》2010,110(5):851-862
A simplified system of equations describing small-amplitude nonlinear quasi-transverse waves in an elastic weakly anisotropic
medium with complicated dissipation and dispersion is considered. A simplified system of equations derived for describing
the propagation and evolution of one-dimensional weakly nonlinear electromagnetic waves in a weakly anisotropic dielectric
is found to be of the same type as the system of equations for quasi-transverse waves in an elastic medium. The steady-state
structure of small-amplitude quasi-transverse discontinuities and a large number of admissible discontinuity types is studied
using this system of equations. Viscous dissipation is traditionally assumed to be described in terms of the next differentiation
order as compared to those constituting the hyperbolic system describing long waves, while the terms responsible for dispersion
have an even higher differentiation order. 相似文献
20.
The generation of a vortex flow by waves on a water surface, which simulate an energy cascade in a system of gravity waves at frequencies of 3, 4, 5, and 6 Hz, has been studied experimentally. It has been found that pumping is accompanied by the propagation of waves on the surface at different angles to the fundamental mode and by a nonlinear interaction between waves resulting in the generation of new harmonics. It has been shown that large-scale flows are formed by modes of the lowest frequency of 3 Hz intersecting at acute angles. The energy distribution of the vortex motion can be described by a power-law function of the wavenumber and is independent of the energy distribution in a system of surface waves. The energy coming to large-scale vortex flows directly from the wave system is transferred to small scales. A direct rather than inverse energy flux is established in the system of vortices. 相似文献