We observe experimentally the self-phase modulation of a surface plasmon-polariton (SPP) propagating along a gold film bounded by air in a Kretschmann-Raether configuration. Through analyzing the power dependence of the reflectance curve as a function of the incidence angle, we characterize the complex-valued nonlinear propagation coefficient of the SPP. Moreover, we present a procedure that ca...

In this article, we present an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result a...

Lie algebraic methods are described which were used to optimize the d~ign of the PEP-II lattices. These methods include calculation of the nonlinear Hamiltonian for lattice modules, dimensionless normalized representation of resonance basis coefficients, correlation of coefficients with dynamic aperture determination, and techniques for coefficient control and compensation.

−∞ log(z− s)d(log(1−|r(s)|2))+ π 4 + argΓ(iν(z))− argr(z). Here z0 = −x/(4t), Γ is the gamma function and the function r is the so-called reflection coefficient associated to the initial data q0, as described later in this section. Estimates on the size of the error term E (x,t) depend on the smoothness assumptions on q0. The above asymptotic form was first obtained in [10]. The nonlinear steep...

In this study the third order nonlinear susceptibilities are theoreticallycalculated for an electron confined in an isolated PbS/ CdSe/ CdS spherical core-shellshellquantum dots. Our calculation is associated with intersubband transitions in theconduction band. We used the effective mass approximation in this study which is asimple and straightforward study of the third-order optical nonlineari...

The Fokker–Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker– Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leadin...