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Variable-coefficient Korteweg - de Vries equation is applied to describe the interfacial wave transformation in two-layer fluid of variable depth. The soliton dynamics in this fluid is studied. The solitary wave breaks in two transient…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects…
Acoustic shock and acceleration waves in inhomogeneous fluids are investigated using both analytical and numerical methods. In the context of start-up signaling problems, and based on linear acoustics theory, we study the propagation of…
We analyze the propagation of an incident electromagnetic wave in a purely-time modulated medium. Precisely, we assume that the permeability is unchanged while the permittivity has a multiple-step profile in time and uniformly constant in…
A problem of amplitude reconstruction in terms of the given angular distribution is considered. Solution of this problem is not unique. A class of amplitudes, correspondent to one and the same angular distribution, forms a region in…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Space-time varying media enable unprecedented control over electromagnetic waves, yet most existing studies assume idealized, nondispersive materials and thus fail to capture the intrinsic frequency dispersion of realistic platforms. Here,…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
In this article, the convergence of a hybrid numerical method introduced in Daripa and Dutta (J. Comput. Phys., 335:249-282, 2017) has been established. This method integrates a discontinuous finite element method with a modified method of…
In this work we present a theoretical study on the propagation of light in heterogeneous systems with fluctuating optical properties. To understand the consequences of the fluctuations we perform numerical calculations with uniform and non…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…
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…
We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.