Search results for " Nonlinear"

Recensione: MR3198633 Reviewed Olszowy, Leszek A family of measures of noncompactness in the space L1loc(R+) and its application to some nonlinear Vo…

2014

MR3112896 Saichev, Alexander I.; Woyczyński, Wojbor A. Distributions in the physical and engineering sciences. Vol. 2. Linear and nonlinear dynamics …

2014

Nonlinearities in the Becker-Tomes-Solon model

2011

The aim of this paper is to explore nonlinearities in the relationship between parents and children earnings. We rst discuss a simple extension of the Becker-Tomes-Solon model accounting for nonlinearity. We then test the linearity of intergenerational transmission employing a set of 141 intergenerational mobility tables in 35 di erent countries at di erent time periods, and nd that linearity is rejected in 89 tables. We nally explore the correlation between the \strength of concavity" and income inequality. Our ndings suggest that more unequal societies tend to have a more concave intergenerational transmission process.

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

2016

The dispersionless Kadomtsev-Petviashvili (dKP) equation $(u_t+uu_x)_x=u_{yy}$ is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation $u_t+uu_x=0$. We show numerically that the solutions to the transformed equation do not develop shocks. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the $(x,y)$ plane, where the solution of the dKP equation exists in a weak sense only, and a…

Simple guidelines to predict self-phase modulation patterns

2018

International audience; We present a simple approach to predict the main features of optical spectra affected by self-phase modulation (SPM), which is based on regarding the spectrum modification as an interference effect. A two-wave interference model is found sufficient to describe the SPM-broadened spectra of initially transform-limited or up-chirped pulses, whereas a third wave should be included in the model for initially down-chirped pulses. Simple analytical formulae are derived, which accurately predict the positions of the outermost peaks of the spectra.

Spectral long-range interaction of temporal incoherent solitons.

2014

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Impact of self-steepening on incoherent dispersive spectral shocks and collapse-like spectral singularities

2014

International audience; Incoherent dispersive shock waves and collapselike singularities have been recently predicted to occur in the spectral evolution of an incoherent optical wave that propagates in a noninstantaneous nonlinear medium. Here we extend this work by considering the generalized nonlinear Schrödinger equation. We show that self-steepening significantly affects these incoherent spectral singularities: (i) It leads to a delay in the development of incoherent dispersive shocks, and (ii) it arrests the incoherent collapse singularity. Furthermore, we show that the spectral collapselike behavior can be exploited to achieve a significant enhancement (by two orders of magnitudes) of…

Compact-like pulse signals in a new nonlinear electrical transmission line

2013

International audience; A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers' equations. This equation admits compact pulse solutions and shares some symmetry properties with the Rosenau-Hyman K(2,2) equation. An exact discrete compactly- supported signal voltage is found for the network and the dissipative effects on the pulse motion analytically studied. Numerical simulations confirm the validity of analytical results and the robustness of these …

Pattern dynamics in a nonlinear electrical lattice

2003

International audience; In this paper, we present experiments using a nonlinear electrical line, modeling the FitzHugh-Nagumo equation, without recovery term. Different patterns are studied according to the para meters of this medium and initial conditions. We then propose to apply these results to the domain of signal processing. We show that erosion and dilation of a binary signal, two kinds,of binarization-one depending on an amplitude threshold, the other on an energetical threshold-and nonlinear filtering allowing noise removal can be obtained in the same medium.

Strong-coupling expansions for the -symmetric oscillators

1998

We study the traditional problem of convergence of perturbation expansions when the hermiticity of the Hamiltonian is relaxed to a weaker symmetry. An elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models. We describe its perturbative features paying particular attention to the strong-coupling regime. Efficient numerical perturbation theory proves suitable for such a purpose.