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...

Given a Riemannian manifold (M,g) and group G of isometries (M,g), we investigate the existence G-invariant positive solutions u:M→R to nonlinear equation Δgu+au=u2⋆(k,s)−1dg(x,Gx0)s+huq−1 where Δg=−divg(∇). The singularity nonlinearity are such that problem is critical for Hardy-Sobolev embeddings. We prove by using Aubin minimization Mountain-Pass lemma Ambrosetti-Rabinowitz. As product our a...

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...