Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Effective nonlinear model of resonant tunneling nanostructures

We introduce a model of a nonlinear double-barrier structure to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where a nonlinear local field interaction is introduced to account for those inelastic scattering phenomena. Resonance peaks seen in the transmission coefficient spectra for the linear case appear shifted to higher energies depending on the magnitude of the nonlinear coupling. Our results are in good agreement with self-consistent solutions of the Schrodinger and Poisson equations. The calculation procedure is seen to be very fast, which makes our technique a good candidate for a rapid approximate analysis of these structures.

Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.