This paper studies the Biswas-Milovic equation with log law nonlinearity. TheGausson solution is obtained by the ansatz method. Subsequently, theconservation laws are derived and the conserved quantities are computed usingthe Gausson solution.

We have studied both experimentally and numerically the dynamic effect of nonlinearity on lasing in disordered medium. The third-order nonlinearity not only changes the frequency and size of lasing modes, but also modifies the laser emission intensity and laser pulse width. When the nonlinear response time is longer than the lifetime of the lasing mode, the nonlinearity changes the laser output...

We propose the use of self-defocusing nonlinearities to control nonlinear phase shifts in soliton fiber lasers. By analogy to dispersion management, we refer to this scheme as nonlinearity management. First we describe a map that can be regarded as a combination of nonlinearity management and dispersion management. The map is designed to support solitons in two segments of alternating sign of n...

A gramians based method for quantifying the nonlinearity of the control-affine spatio-temporal systems is proposed in this paper. The empirical gramians are computed from the data collected from a nonlinear model derived by collocation method for spatio-temporal systems. This method compares the empirical gramians of the nonlinear model with that of the linearized model at its steady state oper...

We use pump-probe spectroscopy and continuous wave cross-phase and cross-amplitude modulation measurements to study the optical nonlinearity of a hydrogenated amorphous silicon (a-Si:H) nanowire waveguide, and we compare the results to those of a crystalline silicon waveguide of similar dimensions. The a-Si:H nanowire shows essentially zero instantaneous two-photon absorption, but it displays a...

In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF (2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlineari...

The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schrödinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical propert...