Search results for "Nonlinear"

ZBL MS 63/6 Satco, Bianca-Renata; Turcu, Corneliu-Octavian Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on t…

2013

The authors prove an existence result for a nonlinear integral equation on time scales under weak topology assumption in the target Banach space. In the setting of vector valued functions on time scales they consider the Henstock-Kurzweil-Pettis $\Delta$-integral which is a kind of Henstock integral recently introduced by Cichon, M. [Commun. Math. Anal. 11 (2011), no. 1, 94�110]. In this framework they show the existence of weakly continuous solutions for an integral equation x(t)= f(t, x(t))+ (HKP)\int_0^t g(t,s,x(s)) \Delta s governed by the sum of two operators: a continuous operator and an integral one. The main tool to get the solutions is a generalization of Krasnosel'skii fixed point…

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

2014

Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems

2020

We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.

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.

MAST solution of irrotational flow problems in 2D domains with strongly unstructured triangular meshes

2010

A new methodology for the solution of irrotational 2D flow problems in domains with strongly unstructured meshes is presented. A fractional time step procedure is applied to the original governing equations, solving consecutively a convective prediction system and a diffusive corrective system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system, of the order of the number of computational cells. A MArching in Space and Time (MAST) approach is applied for the solution of the convective prediction step. The major advantages of the model, as well as its ability to maintain the solution monotonicit…

An experimental investigation of the nonlinear refractive index (n2) of carbon disulfide and toluene by spectral shearing interferometry and z-scan t…

2003

International audience; The recently proposed spectral shear interferometry and the well-known z-scan techniques were employed for the determination of the nonlinear refractive index n2 of CS2, toluene and fused silica. The determined n2 values by both techniques were found to be in very good agreement. In addition, the role of the repetition rate of the laser is also investigated revealing its importance for the correct determination of both the size and the sign of the nonlinearity.

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…

Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves

2018

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrodinger equation in the semiclassical limit.

Observation of Optical Undular Bores in Multiple Four-Wave Mixing

2014

International audience; We demonstrate that wave-breaking dramatically affects the dynamics of nonlinear frequency conversion processes that operate in the regime of high efficiency (strong multiple four-wave mixing). In particular, by exploiting an all-optical-fiber platform, we show that input modulations propagating in standard telecom fibers in the regime of weak normal dispersion lead to the formation of undular bores (dispersive shock waves) that mimic the typical behavior of dispersive hydrodynamics exhibited, e.g., by gravity waves and tidal bores. Thanks to the nonpulsed nature of the beat signal employed in our experiment, we are able to clearly observe how the periodic nature of …