Solitons in a modified discrete nonlinear Schrödinger equation

Area of Science:

• Nonlinear physics
• Condensed matter physics
• Mathematical physics

Background:

• The discrete nonlinear Schrödinger (DNLS) equation models phenomena in nonlinear optics, Bose-Einstein condensates, and other discrete systems.
• Understanding nonlinear modes and discrete solitons is crucial for controlling energy transport in these systems.

Purpose of the Study:

• To investigate the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation.
• To analyze the linear and modulational stability of the lowest-order modes.
• To explore methods for managing the Peierls-Nabarro barrier and steering discrete solitons.

Main Methods:

• Linear stability analysis of nonlinear modes.
• Modulational stability analysis.
• Numerical simulations of soliton dynamics and long-time propagation.

Main Results:

• The fundamental bulk mode of the mDNLS equation does not require a power threshold.
• The fundamental surface mode necessitates a minimum power level for existence.
• Soliton steering is achievable by managing the Peierls-Nabarro barrier in strongly localized modes.
• At long evolution times, nonlinear effects diminish, leading to ballistic propagation.

Conclusions:

• Discrete solitons in the mDNLS model are robust entities capable of excitation transport in generic discrete media.
• The findings have implications for systems modeled by the standard DNLS equation.
• The study provides insights into the behavior and control of nonlinear modes in discrete systems.