Formation, control, and dynamics of N localized structures in the Peyrard-Bishop model

Elías Zamora-Sillero, A. V. Shapovalov, Francisco J. Esteban

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We explore in detail the creation of stable localized structures in the form of localized energy distributions that arise from general initial conditions in the Peyrard-Bishop (PB) model. By means of a method based on the inverse scattering transform we study the solutions of PB model equations obtained in the form of planar waves whose amplitudes are described by the nonlinear Schrödinger equation (NLS). For localized initial conditions different from the pure N -soliton shape, we have obtained analytical results that predict and control the number, amplitude, and velocity of the NLS solitary waves. To verify the validity of these results we have carried out numerical simulations of the PB model with the use of realistic values of parameters and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the NLS. In the simulations we have found that N localized structures arise in agreement with the prediction of the analytical results obtained in the NLS.

Original languageEnglish
Article number066603
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume76
Issue number6
DOIs
Publication statusPublished - 6 Dec 2007

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Localized Structures
Formation Control
nonlinear equations
Nonlinear Equations
Initial conditions
solitary waves
Inverse Scattering Transform
Energy Distribution
inverse scattering
Solitary Waves
Model
Solitons
energy distribution
simulation
Verify
Predict
Numerical Simulation
Prediction
predictions
Form

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Formation, control, and dynamics of N localized structures in the Peyrard-Bishop model. / Zamora-Sillero, Elías; Shapovalov, A. V.; Esteban, Francisco J.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 76, No. 6, 066603, 06.12.2007.

Research output: Contribution to journalArticle

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