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Multipulses in discrete Hamiltonian nonlinear systems.

P G Kevrekidis1

  • 1Program in Applied and Computational Mathematics, Princeton University, Washington Road, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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This study investigates multipulse behavior in discrete nonlinear systems, revealing how discreteness enables stable static configurations unlike their continuous counterparts. Numerical experiments confirm these findings.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Computational science

Background:

  • Discrete Hamiltonian nonlinear systems exhibit complex behaviors.
  • Understanding multipulse configurations is crucial for nonlinear system analysis.
  • Continuum systems often differ significantly from their discrete analogs.

Purpose of the Study:

  • Investigate multipulse behavior in discrete Hamiltonian nonlinear systems.
  • Utilize the discrete nonlinear Schrödinger equation as a benchmark model.
  • Identify key factors governing multipulse dynamics in discrete systems.

Main Methods:

  • Employ a singular perturbation methodology.
  • Implement a variational approach.
  • Conduct numerical experiments for verification.

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Main Results:

  • Both methodologies successfully identified dominant factors in the discrete problem.
  • Discreteness and exponential tail-tail pulse interactions were shown to interplay.
  • Confirmed that discrete systems can sustain static multipulse configurations.

Conclusions:

  • Discrete systems possess unique properties allowing for static multipulse configurations.
  • The findings contrast with the behavior observed in continuum systems.
  • Validated the theoretical findings through numerical simulations.