Related papers: On the solutions of a factorized wave equation
In this paper we investigate the implementation of the so-called freezing method for second order wave equations in one and several space dimensions. The method converts the given PDE into a partial differential algebraic equation which is…
Light propagation is viewed as a process involving mutual creation of electric and magnetic fields. This viewpoint is used to argue that the conventional retarded solutions to electromagnetic wave equations (whose source is a current…
By solving Maxwell's equations the exact dispersion equation for electromagnetic waves propagating in a layered coaxial ferrite line is obtained. In particular the analytical consideration is carried out for a simpler case of complete…
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous chains with a general power-law contact interaction is studied. For this wave equation,…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
The Kawahara equation is a weakly nonlinear long-wave model of dispersive waves that emerges when leading order dispersive effects are in balance with the next order correction. Traveling wave solutions of the Kawahara equation satisfy a…
We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels,…
In this paper, we study the existence and stability of travelling wave solutions of a kinetic reaction-transport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction…
For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian…
Wave equations containing spatial derivatives which are higher than second order arise naturally in the context of condensed matter systems. The solutions of such equations contain more than two modes and consequently, the range of possible…
We study several basic dispersive models with random periodic initial data such that the different Fourier modes are independent random variables. Motivated by the vast Physics literature on related topics, we then study how much the…
The wave propagation problem on a taut cable resting on a bilinear substrate is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to permit…
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.
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
Guided wave propagation through a left-handed medium has been studied, and new physics discovered. The results are based upon ab initio Green's function calculations. Numerically generated dispersion diagrams and field distribution plots…
Wave scattering is considered in a medium in which many small particles are embedded. Equations for the effective field in the medium are derived when the number of particles tends to infinity.
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
In order to settle the problem of the "Post constraint" in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the…
Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…