### Abstract

Original language | English |
---|---|

Journal | Physical Review E. Statistical, Nonlinear, and Soft Matter Physics |

Volume | 55 |

Issue number | 5 |

Pages (from-to) | 6141-6149 |

ISSN | 1063-651X |

DOIs | |

Publication status | Published - 1997 |

### Bibliographical note

Copyright (1997) by the American Physical Society.### Keywords

- SYSTEMS
- BREATHERS
- INTRINSIC LOCALIZED MODES
- POLYACETYLENE
- STABILITY
- RANGE INTERPARTICLE INTERACTIONS
- 2-DIMENSIONAL ANHARMONIC LATTICES
- SOLITON
- DYNAMICS
- NONLINEAR SCHRODINGER-EQUATION

### Cite this

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

*55*(5), 6141-6149. https://doi.org/10.1103/PhysRevE.55.6141

}

*Physical Review E. Statistical, Nonlinear, and Soft Matter Physics*, vol. 55, no. 5, pp. 6141-6149. https://doi.org/10.1103/PhysRevE.55.6141

**Effects of nonlocal dispersive interactions on self-trapping excitations.** / Gaididei, Yu.B.; Mingaleev, S.F.; Christiansen, Peter Leth; Rasmussen, Kim.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Effects of nonlocal dispersive interactions on self-trapping excitations

AU - Gaididei, Yu.B.

AU - Mingaleev, S.F.

AU - Christiansen, Peter Leth

AU - Rasmussen, Kim

N1 - Copyright (1997) by the American Physical Society.

PY - 1997

Y1 - 1997

N2 - A one-dimensional discrete nonlinear Schrodinger (NLS) model with the power dependence r(-s) on the distance r of the dispersive interactions is proposed. The stationary states psi(n) of the system are studied both analytically and numerically. Two types of stationary states are investigated: on-site and intersite states. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the NLS model with a nearest-neighbor interaction. For s less than some critical value s(cr), there is an interval of bistability where two stable stationary states exist at each excitation number N = Sigma(n)\psi(n)\(2). For cubic nonlinearity the bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for intersite solitons is close to 2.1. For increasing degree of nonlinearity sigma, s(cr) increases. The long-distance behavior of the intrinsically localized states depends on s. For s > 3 their tails are exponential, while for 2 <s <3 they are algebraic. In the continuum limit the model is described by a nonlocal MLS equation for which the stability criterion for the ground state is shown to be s <sigma + 1.

AB - A one-dimensional discrete nonlinear Schrodinger (NLS) model with the power dependence r(-s) on the distance r of the dispersive interactions is proposed. The stationary states psi(n) of the system are studied both analytically and numerically. Two types of stationary states are investigated: on-site and intersite states. It is shown that for s sufficiently large all features of the model are qualitatively the same as in the NLS model with a nearest-neighbor interaction. For s less than some critical value s(cr), there is an interval of bistability where two stable stationary states exist at each excitation number N = Sigma(n)\psi(n)\(2). For cubic nonlinearity the bistability of on-site solitons may occur for dipole-dipole dispersive interaction (s = 3), while s(cr) for intersite solitons is close to 2.1. For increasing degree of nonlinearity sigma, s(cr) increases. The long-distance behavior of the intrinsically localized states depends on s. For s > 3 their tails are exponential, while for 2 <s <3 they are algebraic. In the continuum limit the model is described by a nonlocal MLS equation for which the stability criterion for the ground state is shown to be s <sigma + 1.

KW - SYSTEMS

KW - BREATHERS

KW - INTRINSIC LOCALIZED MODES

KW - POLYACETYLENE

KW - STABILITY

KW - RANGE INTERPARTICLE INTERACTIONS

KW - 2-DIMENSIONAL ANHARMONIC LATTICES

KW - SOLITON

KW - DYNAMICS

KW - NONLINEAR SCHRODINGER-EQUATION

U2 - 10.1103/PhysRevE.55.6141

DO - 10.1103/PhysRevE.55.6141

M3 - Journal article

VL - 55

SP - 6141

EP - 6149

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

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

SN - 2470-0045

IS - 5

ER -