The generalized nonlinear Schrödinger (GNLS) equation is solved numerically by a split-step Fourier method. The first, second and fourth-order versions of the method are presented. A classical problem concerning the motion of a single solitary wave is used to compare the first, second and fourth-order schemes in terms of the accuracy and the computational cost. This numerical experiment shows t...

The Colin de Verdière parameters, μ and ν, are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal graphs. For ν the calculation is based solely on maximal cliques, while for μ the calculation depends on split subgraphs. For the case of μ our work extends some recent work on com...

Recently Agarwal and Sood, in their paper entitled “Split (n+ t)−color partitions and Gordon-McIntosh eight order mock theta functions, The Electronic Journal of Combinatorics 21(2), (2014), #P2.46”, have defined and used the ‘split (n+t)−color partitions’ to obtain the combinatorial interpretations of two mock theta functions. The purpose of this paper is to extend their results using ‘signed ...

We discuss a method aimed at reducing the risk that spurious results are published. Researchers send their datasets to an independent third party who randomly generates training and testing samples. Researchers perform their analysis on the former and once the paper is accepted for publication the method is applied to the latter and it is those results that are published. Simulations indicate t...

A wavelet based model for propagation of optical pulses in nonlinear media is presented. We obtain an O(N) algorithm for linear propagation by replacing the wavelet-domain propagation operator by its Taylor series approximation. Nonlinear propagation is then achieved by adding the nonlinear term in mid-step in a method analogous to the split-step Fourier method. Using wavelets ooers the advanta...

A 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented and implemented on a parallel compute cluster. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for c...

The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domai...

The computer program spip is aimed at solving the Generalized Non-Linear Schrödinger equation (GNLSE), involved in optics e.g. in the modelling of light-wave propagation in an optical fibre, by the Interaction Picture method, a new efficient alternative method to the Symmetric Split-Step method. In the spip program a dedicated costless adaptive step-size control based on the use of a 4th order ...

We show the necessary condition for Higgs mass parameters in order for the recently proposed “split supersymmetry” (split-SUSY) scenario to provide the realistic magnitude of tan β. This can be understood by showing how the Higgs sector of the minimal supersymmetric Standard Model reduces to that of the Standard Model in the heavy limit of the soft supersymmetry breaking Higgs mass parameters. ...