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Envelope solitons on anharmonic damped atomic chains.

C Brunhuber1, F G Mertens, Y Gaididei

  • 1Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany. christian.brunhuber@uni-bayreuth.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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This study examines how damping affects envelope solitons in anharmonic chains. The quasi-continuum approximation accurately predicts soliton behavior under damping, outperforming the continuum model.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Soliton theory

Background:

  • Envelope solitons are crucial in nonlinear systems.
  • Understanding dissipation's impact on solitons is vital for accurate modeling.
  • Anharmonic chains provide a discrete model for wave propagation.

Purpose of the Study:

  • To investigate the influence of Stokes and hydrodynamical damping on envelope solitons.
  • To derive and compare evolution equations in continuum and quasi-continuum approximations.
  • To analyze the effect of damping on soliton shape using collective variables.

Main Methods:

  • Derivation of envelope evolution equations for continuum and quasi-continuum models.
  • Introduction of a collective variable ansatz to describe damping effects.

Related Experiment Videos

  • Derivation of ordinary differential equations for amplitude, width, and chirp.
  • Comparison of analytical results with numerical simulations of discrete systems.

    • Main Results:

    • Analytical models for damping effects on envelope solitons were developed.
    • The quasi-continuum approximation showed improved accuracy over the continuum approximation.
    • Collective variable evolution equations successfully described soliton spatial modulation.
    • High agreement was found between analytical predictions and simulations for high-energy excitations.

    Conclusions:

    • The quasi-continuum approximation offers a more accurate description of damped solitons on anharmonic chains.
    • Collective variable methods effectively capture the dynamics of soliton shape under dissipation.
    • This research provides improved analytical tools for studying nonlinear wave phenomena in discrete systems.