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We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. Of particular…
The geometrical diffraction theory, in the sense of Keller,is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the diffracted…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine…
We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the…
In this paper we develop a reduction procedure for determining exact wave solutions of first order quasilinear hyperbolic one-dimensional nonhomogeneous systems. The approach is formulated within the theoretical framework of the method of…
When wind blows over water, ripples are generated on the water surface. These ripples can be regarded as perturbations of the wind field, which is modelled as a parallel inviscid flow. For a given wavenumber $k$, the perturbed…
In this paper, we show that a general method introduced by Fu and Mielke allows to give a complete answer on the existence and uniqueness of a subsonic solution describing the propagation of surface waves in an isotropic half space modelled…
The condition for potential description of the wake waves,generated by flat or cylindrical driving electron bunch in cold plasma is derived. The two-dimensional nonlinear equation for potential valid for small values of that is obtained and…
Metamaterials are artificially structured media that can focus (lensing) or reroute (cloaking) waves, and typically this is developed for electromagnetic waves at millimetric down to nanometric scales or for acoustics or thin elastic plates…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic…
We study normal modes for the linear water wave problem in infinite straight channels of bounded constant cross-section. Our goal is to compare semianalytic normal mode solutions known in the literature for special triangular…
We derive the formal solution to the dispersion relation for linear surface waves on a horizontal mean current with arbitrary vertical dependence. The problem is cast in a Green's function framework for the Rayleigh equation, neglecting…
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in…
This works deals with one dimensional infinite perturbation - namely line defects - in periodic media. In optics, such defects are created to construct an (open) waveguide that concentrates light. The existence and the computation of the…
In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with…
We consider the propagation of waves in a waveguide with Neumann boundary conditions. We work at low wavenumber with only one propagating mode in the leads, all the other modes being evanescent. We assume that the waveguide is symmetric…
The propagation of acoustic waves in a poro-elastic medium of infinite extension containing spherical cavities randomly distributed is investigated. The scattering coefficients are computed in the low frequency limit using the sealed pore…