Abstract
We study the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls-Nabarro barrier, facilitating in this way a degree of soliton steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The qualitative similarity of the results for the mDNLS to the ones obtained for the standard DNLS, suggests that this kind of discrete soliton is an robust entity capable of transporting an excitation across a generic discrete medium that models several systems of interest.
Highlights
In the semiclassical approach to the coupled electron-phonon problem, the electronic degrees of freedom are coupled to the vibrational ones, where the latter are pictured as classical oscillators
On the other hand, when the oscillators are taken as of the Debye, or acoustic type, one arrives to the less-known Modified Discrete Nonlinear equation: i dCn dt Hereafter, we will dispense with the physical origin of the modified one-dimensional discrete nonlinear Schrödinger (mDNLS) and proceed to focus on its selftrapping and transport properties, and show that its soliton phenomenology is similar to the one found previously in DNLS
We have studied the nonlinear bulk and surface modes of the modified discrete nonlinear Schrödinger equation
Summary
We study the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation. We will dispense with the physical origin of the mDNLS and proceed to focus on its selftrapping and transport properties, and show that its soliton phenomenology is similar to the one found previously in DNLS This is very important since it supports the idea that a discrete soliton is a robust excitation of the system, regardless of the precise nature of the underlying vibrational degrees of freedom. In this sense, the DNLS and mDNLS can be regarded as complementary equations. In this work we will focus on the different families of nonlinear bulk and surface modes and their stability properties, transport exponents and on the propagation of mDNLS solitons, looking for possible means of propagation control
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