It is well known that a symmetric soliton in coupled nonlinear Schrödinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of the energy, featuring a transition into an asymmetric soliton via a subcritical bifurcation. A similar phenomenon was found in a...

Consider a uniform train of surface waves with a two-dimensional, bi-periodic surface pattern, propagating on deep water. One approximate model of the evolution of these waves is a pair of coupled nonlinear Schrödinger equations, which neglects any dissipation of the waves. We show that in this...

The problem of the modulational instability (MI) of electron-acoustic waves (EAWs) in a plasma with Cairns–Tsallis distributed electrons is addressed. Using the standard multiple scale method, we derive a nonlinear Schrödinger-like equation. Electron nonextensivity and nonthermality are found...

The variational approach to Bayesian inference enables simultaneous estimation of model parameters and model complexity. An interesting feature of this approach is that it also leads to an automatic choice of model complexity. Empirical results from the analysis of hidden Markov models with...

We consider a dynamical model of a superfluid Fermi gas in the Bardeen–Cooper–Schrieffer regime trapped in a periodic optical lattice (OL) potential. The model is based on an equation for complex order parameter ϕ of the superfluid, which is derived from the relevant energy density and...

We report on the time dependent solutions of the q-generalized Schrödinger equation proposed by Nobre et al. (2011). Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work...

In this report we present numerical simulations of nonlinear pulse propagation in air to elucidate the physical mechanism underlying the experimentally observed long distance propagation of filaments. Simulations of the nonlinear Schrödinger equation for the electromagnetic field coupled to the...

We explore spatially extended dynamical states in the discrete nonlinear Schrödinger lattice in two- and three-dimensions, starting from the anti-continuum limit. We first consider the “core” of the relevant states (either a two-dimensional “tile” or a three-dimensional “stone”),...