Related papers: Travelling waves for Maxwell's equations in nonlin…
This paper is concerned with the traveling wave solutions for integro-difference systems of higher order. By using Schauder fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and…
Using the ``composite harmonic mapping method," we construct exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of…
In general, Maxwell's equations require that a wave of magnetic field be accompanied by a wave of electric field, and vice versa. In magnetic media it is possible to have waves of magnetization with negligible electric field. We discuss an…
Of concern is the a priori symmetry of traveling wave solutions for a general class of nonlocal dispersive equations \[ u_t +(u^2 +Lu)_x =0, \] where $L$ is a Fourier multiplier operator with symbol $m$. Our analysis includes both…
We establish the existence of quasi-periodic traveling wave solutions for the $\beta$-plane equation on $\mathbb{T}^2$ with a large quasi-periodic traveling wave external force. These solutions exhibit large sizes, which depend on the…
In this paper, we study the existence of traveling waves for a fourth order Schr\" odinger equations with mixed dispersion, that is, solutions to $$\Delta^2 u +\beta \Delta u +i V \nabla u +\alpha u =|u|^{p-2} u,\ in\ \R^N ,\ N\geq 2.$$ We…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE-modes which are localized in space directions orthogonal to…
In this paper, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We…
We find exact solutions to Maxwell equations written in terms of four-vector potentials in non--rotating, as well as in G\"odel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential…
We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…
We consider in the paper axially-symmetric and stationary fields and cylindrically symmetric gravito-electromagnetic waves in the Nonsymmetric Kaluza-Klein Theory.Using symbollic manipulations we write down all important quantities in the…
The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…
Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying…
We develop a unified perspective of unidirectional topological edge waves in non-reciprocal media. We focus on the inherent role of photonic spin in non-reciprocal gyroelectric media, ie. magnetized metals or magnetized insulators. We first…
Following a general principle introduced by Ehrnstr\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.
We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in…
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,…
Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation…