Soliton trapping in a disordered lattice.

Area of Science:

• Nonlinear dynamics
• Soliton physics
• Statistical mechanics

Background:

• The Ablowitz-Ladik model is an integrable system exhibiting stable solitons without external potentials.
• The interplay between nonlinearity and randomness is a key area of research in complex systems.
• Understanding soliton behavior in disordered environments is crucial for various physical applications.

Purpose of the Study:

• To investigate the dynamics of Ablowitz-Ladik solitons under the influence of a random potential.
• To analyze the stability and particle-like properties of solitons in the presence of disorder.
• To identify predictive mechanisms for soliton motion, including changes in direction.

Main Methods:

• Numerical simulations of the Ablowitz-Ladik model with a random potential.
• Analysis of soliton trajectories and mass variations over time.
• Derivation of an effective potential to describe soliton dynamics.

Main Results:

• The random potential destroys the inherent stability of the solitons.
• Two distinct regimes of particle-like dynamics were observed: one with constant mass and another with varying mass.
• An effective potential was derived, accurately predicting changes in the soliton's direction of motion.
• This effective potential exhibits scaling behavior with time and potential strength.

Conclusions:

• Random potentials significantly alter the dynamics of Ablowitz-Ladik solitons, leading to instability.
• The study reveals complex particle-like behaviors and introduces a predictive effective potential for soliton dynamics.
• A direct relationship was established between the soliton's first direction reversal time and the strength of the random potential.