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An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like…
An inverse scattering problems for the 3-D generalized Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. Uniqueness theorem is proved.
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to…
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential…
It is proved that a connected polygonal obstacle coated by thin layers together with its surface impedance function can be determined uniquely from the far field pattern of a single incident plane wave. Our proof is based on the Schwarz…
Vector calculus in three dimensions with a Euclidian metric is the lingua franca of classical physics, including classical electrodynamics. This article corrects some long-standing imprecision in a fundamental result. Some textbooks assert…
We consider the wave propagation in media with step-like inhomogeneities. We choose two different protocols: (I) a step-like spatial dependence of the coupling constant that physically corresponds to the junction of two systems and (II) the…
Rayleigh-Bloch waves are guided acoustic waves propagating along a periodic line of inclusions placed inside an open, infinite medium. Below the sound cone, they are transversely evanescent on both sides of the line of inclusions. Guidance…
Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex…
The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
This paper establishes a complete time-harmonic scattering theory for hyperbolic space, formulating it within the classical Sommerfeld-Rellich paradigm centered on far-field patterns--a foundational framework that has been absent despite…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…
In the junction $\Omega$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[\lambda_\dagger, +\infty)$ with a positive cut-off value $\lambda_\dagger$. We give two…
The paper contains a simplified and improved version of the results obtained by the authors earlier. Wave propagation is discussed in a network of branched thin wave guides when the thickness vanishes and the wave guides shrink to a one…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behavior at infinity is established. Some generalizations to nonautonomous radial…
We present a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static, spherically symmetric black hole spacetimes, developed entirely within Schwarzschild-like coordinates. Start ing from the…