### Выдержка

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 SchrÃ¶dinger 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.

Язык оригинала | Английский |
---|---|

Номер статьи | 066603 |

Журнал | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Том | 76 |

Номер выпуска | 6 |

DOI | |

Состояние | Опубликовано - 6 дек 2007 |

### Отпечаток

### ASJC Scopus subject areas

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

### Цитировать

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*76*(6), [066603]. https://doi.org/10.1103/PhysRevE.76.066603

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

Результат исследований: Материалы для журнала › Статья

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, том. 76, № 6, 066603. https://doi.org/10.1103/PhysRevE.76.066603

}

TY - JOUR

T1 - Formation, control, and dynamics of N localized structures in the Peyrard-Bishop model

AU - Zamora-Sillero, Elías

AU - Shapovalov, A. V.

AU - Esteban, Francisco J.

PY - 2007/12/6

Y1 - 2007/12/6

N2 - 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 SchrÃ¶dinger 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.

AB - 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 SchrÃ¶dinger 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.

UR - http://www.scopus.com/inward/record.url?scp=36849048702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36849048702&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.066603

DO - 10.1103/PhysRevE.76.066603

M3 - Article

AN - SCOPUS:36849048702

VL - 76

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 6

M1 - 066603

ER -