We investigate nonlinear propagation in the presence of the optical Kerr effect by relying on a rigorous generalization of the standard parabolic equation that includes nonparaxial and vectorial terms. We show that, in the (1 + 1)-D case, both soliton and propagation-invariant pattern solutions exist (while the standard hyperbolic-secant function is not a solution).

The Fibonacci secant function is constructed in this paper. Fibonacci tan-sec method is presented to search for the exact traveling wave solutions of nonlinear differentialdifference equations (DDEs). This method is essentially equivalent to the classical hyperbolic method. The discrete mKdV lattice and some other lattice equations are chosen to illustrate the efficiency and effectiveness of th...

We shall first review some non-normal stationary first-order autoregressive models. The models are constructed with a given marginal distribution (logistic, hyperbolic secant, exponential, Laplace, or gamma) and the requirement that the bivariate joint distribution of the generated process must be sufficiently simple so that the parameter estimation and forecasting problems of the models can be...

This paper is concerned with the Monte Carlo numerical computation of the Laplace transform of exponential Brownian functionals. In addition to the implementation of standard integral formulas, we investigate the use of various probabilistic representations. This involves in particular the simulation of the hyperbolic secant distribution and the use of several variance reduction schemes. The pe...

We investigate the effect of delayed nonlinear response time on pulse compression, using an organic crystal-cored fiber in the normal dispersion region. With up to third-order phase compensation, a 100-W, 100-fs hyperbolic-secant pulse is compressed to ~10 fs with a delayed nonlinear response time as well as without it. It is shown that third-order phase adjustment can compensate for the phase ...

We draw here on the relation between the Cauchy and hyperbolic secant distributions to prove that the MLE of the scale parameter of Cauchy distribution is log-normally distributed and to study the properties of a Hodges-Lehmann type estimator for the scale parameter. This scale estimator is slightly biased but performs well even on small samples regardless of the location parameter. The asympto...

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish no...

We demonstrate the generation of 68 fs secant hyperbolic pulses at a 105 MHz repetition rate with an average power of 520 mW from a diode-pumped Yb(3+):CaGdAlO(4) mode-locked laser. A semiconductor saturable absorber allows passive mode locking, and a 15 W diode laser is used to pump directly the crystal. To our knowledge this represents the highest average power ever obtained for a sub-100 fs ...