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Soliton mobility in disordered lattices.

Zhi-Yuan Sun1, Shmuel Fishman1, Avy Soffer2

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Summary
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We studied how solitons move in disordered Ablowitz-Ladik (AL) and nonlinear Schrödinger (NLS) models using a new potential. Disorder and lattice effects impact soliton mobility, but specific randomness or soliton pairs can enhance transport.

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Area of Science:

  • Nonlinear physics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Soliton dynamics are crucial in nonlinear systems.
  • Disorder and lattice effects can impede soliton mobility.
  • Existing models often simplify these complex interactions.

Purpose of the Study:

  • To investigate soliton mobility in disordered Ablowitz-Ladik (AL) and nonlinear Schrödinger (NLS) lattices.
  • To analyze the impact of an effective potential on soliton dynamics.
  • To propose methods for enhancing soliton transport in disordered systems.

Main Methods:

  • Development and application of an effective potential generalizing the Peierls-Nabarro potential.
  • Statistical analysis of the effective potential's properties.
  • Numerical simulations of soliton dynamics.

Main Results:

  • The effective potential quantifies deviations from integrability due to randomness and discreteness.
  • Soliton mobility is shown to be dependent on the statistical properties and size of the effective potential.
  • The study demonstrates the utility of the effective potential in understanding soliton dynamics.

Conclusions:

  • Specific realizations of randomness and the use of soliton pairs can enhance soliton transport.
  • The developed effective potential provides a valuable tool for studying soliton mobility in disordered systems.
  • Findings offer insights into controlling soliton behavior in complex physical models.