Related papers: Nonlinear surface plasmons
In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
We study the long-time behavior of localized solutions to linear or semilinear parabolic equations in the whole space $\mathbb{R}^n$, where $n \ge 2$, assuming that the diffusion matrix depends on the space variable $x$ and has a finite…
A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed…
We demonstrate that soliton-plasmon bound states appear naturally as propagating eigenmodes of nonlinear Maxwell's equations for a metal/dielectric/Kerr interface. By means of a variational method, we give an explicit and simplified…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on…
Propagation of extremely short unipolar pulses of electromagnetic field ("videopulses") is considered in the framework of a model in which the material medium is represented by anharmonic oscillators (approximating bound electrons) with…
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide…
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…
We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media.…
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma and an ideal plasma slab by using a general, unifying procedure, based on equations of motion, Maxwell's equations and suitable boundary conditions.…
We develop a direct method for solving a modified Camassa-Holm equation with cubic nonlinearity and linear dispersion under the rapidly decreasing vanishing boundary condition. We obtain a compact parametric representation for the…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
Properties of plasmonic materials are associated with surface plasmons - the electromagnetic excitations coupled to coherent electron charge density oscillations on a metal/dielectric interface. Although decay of such oscillations cannot be…
In the present analysis we study the self consistent propagation of nonlinear electromagnetic pulses in a one dimensional relativistic electron-ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian…
Weakly nonlinear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically nonlinear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary…
The nonlinear evolution of a unstable electrostatic wave is considered for a multi-species Vlasov plasma. From the singularity structure of the associated amplitude expansions, the asymptotic features of the electric field and distribution…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…