Transmission of waves by a nonlinear random medium

We study analytically and numerically the effect of nonlinearity on transmission of waves through a random medium. We introduce and analyze quantities associated with the scattering problem that clarify the lack of uniqueness due to the nonlinearity as well as the localization of waves due to the random inhomogeneities. We show that nonlinearity tends to delocalize the waves and that for very large scattering regions the average transmitted energy is small.     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

Nonlinear magnetoinductive waves and domain walls in composite metamaterials

We describe novel physics of nonlinear magnetoinductive waves in left-handed composite metamaterials. We derive the coupled equations for describing the propagation of magnetoinductive waves, and show that in the nonlinear regime the magnetic response of a metamaterial may become bistable. We analyze modulational instability of different nonlinear states, and also demonstrate that nonlinear metamaterials may support the propagation of domain walls (kinks) connecting the regions with the positive and negative magnetization.     

Nearly linear dynamics of nonlinear dispersive waves

Dispersive averaging effects are used to show that the Korteweg-de Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.     

Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

A new exactly solvable ($1+1$)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.     

Quantum effects of nonlinear spin waves in ferromagnets

We investigate a squeezed thermal spin state of nonlinear spin waves in Heisenberg ferromagnets. In this state, the magnon system possesses a new kind of quasiparticle, the dressed magnon, whose mass is a monotonically decreasing function of temperature. The noise of one spin component in the squeezed thermal spin state can be below the noise level in the vacuum state. The magnon system undergoes a first-order phase transition from the normal state to the squeezed thermal spin state. The critical temperature is much lower than the Curie temperature. A possible detection scheme based on a polarized neutron-scattering technique is suggested.     

Transformation of nonlinear sawtooth waves in a medium with refractive inhomogeneities

Theexact solutions of intensive sawtooth waves and beams in a medium with a sound speed inhomogeneity have been found. It has been shown that the focusing on the medium inhomogeneity is strongly pronounced for a single pulse, resulting in the formation of narrow high-amplitude areas. It has been determined that the refractive infomogeneity can lead to a shift of the amplitude maximum of the initial focused beam and the transformation of the converging beam into a dispersing one.     

Interactions of dispersive shock waves

Collisions and interactions of dispersive shock waves in defocusing (repulsive) nonlinear Schrödinger type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counterpropagating dispersive shock waves experience a head-on collision, interact and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schrödinger equation. The boundaries between the background density, dispersive shock waves and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves have some qualitative similarities to the interactions of two classical shock waves.     

Periodic waves in nonlinear metamaterials

Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution.     

Quasi-linear relativistic treatment of electron cyclotron fluctuations in a magnetized plasma

Summary The relativistic quasi-linear theory of electron cyclotron fluctuations is developed for a homogeneous plasma. Expressions are given for the absorption and emission coefficients, consistently with the currently employed linear theory. The extension to the inhomogeneousplasma case is considered and shown to allow the analysis of wave propagation, absorption and emission in plasmas of physical interest.

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Riassunto Si sviluppa la teoria quasi lineare relativistica per le fluttuazioni di onde elettroniche di ciclotrone per un plasma omogeneo. Si otteggono inoltre le espressioni dei coefficienti d'assorbimento ed emissione del plasma, consistentemente con la teoria lineare correntemente usata. Si considera infine l'estensione della teoria ad un plasma disomogeneo, applicandola all'analisi quantitativa di propagazione, assorbimento ed emissione di onde di ciclotrone.

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Резюме Для однородной плазмы развивается релятивистская квазилинейная теория электронных циклотронных флуктуаций. Приводятся вйражения для коэффициентов поглощения и испускания, соответствующих повсеместно используемой линейной теории. Рассматривается обобщения и излучения волн в плазме в физическн интересных случаях.

     

Air-coupled detection of nonlinear Rayleigh surface waves to assess material nonlinearity

This research presents a new technique for nonlinear Rayleigh surface wave measurements that uses a non-contact, air-coupled ultrasonic transducer; this receiver is less dependent on surface conditions than laser-based detection, and is much more accurate and efficient than detection with a contact wedge transducer. A viable experimental setup is presented that enables the robust, non-contact measurement of nonlinear Rayleigh surface waves over a range of propagation distances. The relative nonlinearity parameter is obtained as the slope of the normalized second harmonic amplitudes plotted versus propagation distance. This experimental setup is then used to assess the relative nonlinearity parameters of two aluminum alloy specimens (Al 2024-T351 and Al 7075-T651). These results demonstrate the effectiveness of the proposed technique – the average standard deviation of the normalized second harmonic amplitudes, measured at locations along the propagation path, is below 2%. Experimental validation is provided by a comparison of the ratio of the measured nonlinearity parameters of these specimens with ratios from the absolute nonlinearity parameters for the same materials measured by capacitive detection of nonlinear longitudinal waves.     

Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

非线性兰姆波在厚度缓慢变化和衰减下的特性分析

该文运用解析的方式推导了考虑声波衰减时兰姆波二次谐波的累积和传播规律,并用半解析方式将该理论推广到缓慢变厚度板的情况。由于色散特性,兰姆波二次谐波和基频波相速度不匹配,传播通常会产生拍频效应,使得二次谐波的振幅沿着传播距离周期性的归零。当考虑声波衰减或板的厚度缓慢变化的情况时,拍频效应将不再严格地被满足。二次谐波的振幅依然会沿着传播距离而振荡,但不会归零。该研究可以用于分析如何高效地激发和接收兰姆波的二次谐波,表征和评估不同厚度变化的结构中的微观结构损伤。     

Numerical simulation of three-dimensional nonlinear water waves

We present an accurate and efficient numerical model for the simulation of fully nonlinear (non-breaking), three-dimensional surface water waves on infinite or finite depth. As an extension of the work of Craig and Sulem [19], the numerical method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving surface quantities alone. This is accomplished by introducing the Dirichlet–Neumann operator which is described in terms of its Taylor series expansion in homogeneous powers of the surface elevation. Each term in this Taylor series can be computed efficiently using the fast Fourier transform. An important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the Hamiltonian equations of motion, as well as detailed numerical tests on the convergence of the Dirichlet–Neumann operator. The performance of the model is illustrated by simulating the long-time evolution of two-dimensional steadily progressing waves, as well as the development of three-dimensional (short-crested) nonlinear waves, both in deep and shallow water.     

Nonlinear interaction of a Gaussian EM beam with an electrostatic upper hybrid wave: Stimulated Raman scattering

Summary In this paper we have studied the nonlinear interaction of a Gaussian electromagnetic beam with an electrostatic upper hybrid wave in a collisionless magnetized plasma. On account of the interaction of the incident Gaussian electromagnetic beam with the plasma, a time-independent component of the ponderomotive force becomes finite and leads to the modification in the background density. This results in the excitation of the upper hybrid mode of the plasma. The excited electrostatic wave leads to the enhanced Raman backscattering. An expression for the scattered power is derived and the effect of the external static magnetic field on the enhancement of the density perturbation and scattered power is discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.     

Surface waves at the interface between a metal and a photovoltaic-photorefractive crystal

We investigate surface waves at the interface between a metal and a photovoltaic-photorefractive (PP) crystal. These surface waves appear in several forms: delocalized surface waves, shock surface waves, and localized surface waves. Only localized surface waves have limited energy. We demonstrate that the transverse sizes of localized surface waves decrease with an increase in the propagation constant and the amplitudes of localized surface waves increase with the propagation constant. The stability of localized surface waves is investigated numerically and it is found that they are stable.