### Abstract

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

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

Volume | 54 |

Issue number | 5 |

Pages (from-to) | 5788-5801 |

ISSN | 1063-651X |

DOIs | |

Publication status | Published - 1996 |

### Bibliographical note

Copyright (1996) American Physical Society.### Keywords

- SYSTEMS
- INTRINSIC LOCALIZED MODES
- FRENKEL-KONTOROVA MODEL
- LATTICES
- EXCITATIONS
- PROPAGATION
- MOLECULAR CHAINS
- GAP SOLITONS
- INTEGRABLE MAPPINGS
- ANTIINTEGRABILITY

### Cite this

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

*54*(5), 5788-5801. https://doi.org/10.1103/PhysRevE.54.5788

}

*Physical Review E. Statistical, Nonlinear, and Soft Matter Physics*, vol. 54, no. 5, pp. 5788-5801. https://doi.org/10.1103/PhysRevE.54.5788

**Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.** / Rasmussen, Kim; Henning, D.; Gabriel, H.; Bülow, A.

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

TY - JOUR

T1 - Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

AU - Rasmussen, Kim

AU - Henning, D.

AU - Gabriel, H.

AU - Bülow, A.

N1 - Copyright (1996) American Physical Society.

PY - 1996

Y1 - 1996

N2 - We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest is paid to the creation of stationary localized solutions called breathers. To tackle this problem we apply a map approach and illuminate the linkage of homoclinic and heteroclinic map orbits with localized lattice solutions. The homoclinic and heteroclinic orbits correspond to exact nonlinear solitonlike eigenstates of the lattice. Normal forms and the Melnikov method are used for analytical determinations of homoclinic orbits. Nonintegrability of the map leads to soliton pinning on the lattice. The soliton pinning energy is calculated and it is shown that it can be tuned by varying the ratio of the nonintegrability parameter versus the integrability parameter. The heteroclinic map orbit is derived on the basis of a variational principle. Finally, we use homoclinic and heteroclinic orbits as initial conditions to excite designed stationary localized solutions of desired width in the dynamics of the discrete nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.

AB - We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest is paid to the creation of stationary localized solutions called breathers. To tackle this problem we apply a map approach and illuminate the linkage of homoclinic and heteroclinic map orbits with localized lattice solutions. The homoclinic and heteroclinic orbits correspond to exact nonlinear solitonlike eigenstates of the lattice. Normal forms and the Melnikov method are used for analytical determinations of homoclinic orbits. Nonintegrability of the map leads to soliton pinning on the lattice. The soliton pinning energy is calculated and it is shown that it can be tuned by varying the ratio of the nonintegrability parameter versus the integrability parameter. The heteroclinic map orbit is derived on the basis of a variational principle. Finally, we use homoclinic and heteroclinic orbits as initial conditions to excite designed stationary localized solutions of desired width in the dynamics of the discrete nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.

KW - SYSTEMS

KW - INTRINSIC LOCALIZED MODES

KW - FRENKEL-KONTOROVA MODEL

KW - LATTICES

KW - EXCITATIONS

KW - PROPAGATION

KW - MOLECULAR CHAINS

KW - GAP SOLITONS

KW - INTEGRABLE MAPPINGS

KW - ANTIINTEGRABILITY

U2 - 10.1103/PhysRevE.54.5788

DO - 10.1103/PhysRevE.54.5788

M3 - Journal article

VL - 54

SP - 5788

EP - 5801

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 -