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Averaging of nonlinearity-managed pulses.

Vadim Zharnitsky1, Dmitry Pelinovsky

  • 1Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. vz@math.uiuc.edu

Chaos (Woodbury, N.Y.)
|October 29, 2005
PubMed
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This study analyzes the nonlinear Schrodinger equation for Bose-Einstein condensates using averaging theory. It derives a Hamiltonian averaged equation to approximate nonlinearity-managed solitons.

Area of Science:

  • Quantum physics
  • Nonlinear dynamics
  • Atomic physics

Background:

  • Bose-Einstein condensates (BECs) are quantum states of matter.
  • Feshbach resonance allows for control of interactions in BECs.
  • Nonlinear Schrodinger equation (NLSE) models BEC behavior.

Purpose of the Study:

  • To analyze the NLSE with nonlinearity management for BECs.
  • To derive and validate a Hamiltonian averaged equation.
  • To approximate nonlinearity-managed solitons.

Main Methods:

  • Averaging theory
  • Hamiltonian mechanics
  • Analytical approximation

Main Results:

  • Derivation of a Hamiltonian averaged equation.

Related Experiment Videos

  • Comparison with existing averaging methods.
  • Analytical approximations for nonlinearity-managed solitons.

    • Conclusions:

    • The derived Hamiltonian averaged equation is effective for analyzing nonlinearity-managed solitons in BECs.
    • Averaging theory provides a robust framework for this problem.