The use of the sine-Gordon equation as a model of magnetic flux propagation in Josephson junctions motivates studying the initial-value problem for this equation in the semiclassical limit in which the dispersion parameter ε tends to zero. Assuming natural initial data having the profile of a moving −2π kink at time zero, we analytically calculate the scattering data of this completely integrab...

In this paper, we introduce nonlinear large-signal scattering ( [Formula: see text]) parameters, a new type of frequency-domain mapping that relates incident and reflected signals. We present a general form of nonlinear large-signal [Formula: see text]-parameters and show that they reduce to classic [Formula: see text]-parameters in the absence of nonlinearities. Nonlinear large-signal impedanc...

We show that high efficiency stimulated Raman scattering can be obtained using hollow core photonic crystal fiber with the core filled with a low refractive index nonlinear liquid. This new architecture opens new perspectives in the development of nonlinear functions as any kind of nonlinear liquid media can now be used to implement them, with original properties not accessible with silica core...

Analysis of tides and internal waves from model studies in the South China Sea is done using three techniques. We summarize results from standard Fourier methods, continuous wavelet analysis and the direct scattering transform. Because the Fourier and wavelet analysis are inherently linear methods their utility in application to nonlinear dynamics is often questioned. Nevertheless, they have sh...

An application of the method of approximate inverse to a two-dimensional inverse scattering problem is discussed. The determination of the refractive index from an inverse scattering experiment is a nonlinear inverse problem. In this paper we treat the 2D scalar case. We propose to split this nonlinear problem into an ill-posed linear problem and a (well-posed) nonlinear part by rst solving the...

An application of the method of approximate inverse to a two-dimensional inverse scattering problem is discussed. The determination of the refractive index from an inverse scattering experiment is a nonlinear inverse problem. In this paper we treat the 2D scalar case. We propose to split this nonlinear problem into an ill-posed linear problem and a (well-posed) nonlinear part by rst solving the...

We consider emission of a photon by an electron in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects...

We study the nonlinear Schrödinger equations with a linear potential. A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential.