Search results for " Nonlinearity"
showing 10 items of 33 documents
Spatial beam cleaning in quadratic nonlinear medium
2018
We show experimentally that a laser beam scrambled by propagation in a short segment of multimode fiber may be cleaned by the nonlinear propagation in KTP cristal with type-II second-harmonic generation.
Role of noise in a market model with stochastic volatility
2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES ef…
On the modeling of nonlinear interactions in large complex systems
2010
Abstract This work deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. The contents are specifically focused on the modeling of nonlinear interactions which is one of the most important issues in the mathematical approach to modeling and simulating complex systems, and which includes a learning–hiding dynamics. Applications are focused on the modeling of complex biological systems and on immune competition.
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
2011
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
El tipo de cambio real dólar-euro y el diferencial de intereses reales
2006
This paper investigates whether threshold effects exist in the relationship between dollar-euro real exchange rate and real interest differential, over the period January 1984 to December 2004. We specify a three-regime threshold model and the results provide evidence that there is no threshold effect in the short term, but the nonlinear behaviour of real exchange rate implies threshold effect in the long term. On the other hand, the nonlinearity into the behaviour of real exchange rates can be modelled by a Band-TAR which implies a symmetric response to the real interest differential outside the bank. Finally, into the threshold band the behaviour of real exchange rate is near to follow a …
Inelastic scattering and interactions of three-wave parametric solitons.
2006
We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.
Pulse Generation and Shaping Using Fiber Nonlinearities
2017
Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity
2022
AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal diffe…
Incoherent solitons generated in instantaneous response nonlinear Kerr media
2004
We show theoretically and experimentally in an optical fiber system, that incoherent domain wall solitons can be generated spontaneously from incoherent light, despite of the instantaneous response of the fiber Kerr nonlinearity.