# Ground-state properties of small-size nonlinear dynamical lattices

## Abstract

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground-state (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.

- Authors:

- Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)
- Department of Mathematics and Statistics, University of Massachusetts, Amherst Massachusetts 01003-4515 (United States)
- Dipartimento di Fisica and CNR-INFM, Universita degli Studi di Parma, Parco Area delle Scienze 7/a, I-43100 Parma (Italy)

- Publication Date:

- OSTI Identifier:
- 21072276

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.75.016212; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; BOSE-EINSTEIN CONDENSATION; COUPLING; GROUND STATES; INSTABILITY; LATTICE FIELD THEORY; MATHEMATICAL SOLUTIONS; NONLINEAR OPTICS; NONLINEAR PROBLEMS; PULSES; SCHROEDINGER EQUATION; WAVEGUIDES

### Citation Formats

```
Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A.
```*Ground-state properties of small-size nonlinear dynamical lattices*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.016212.

```
Buonsante, P., Penna, V., Kevrekidis, P. G., & Vezzani, A.
```*Ground-state properties of small-size nonlinear dynamical lattices*. United States. doi:10.1103/PHYSREVE.75.016212.

```
Buonsante, P., Penna, V., Kevrekidis, P. G., and Vezzani, A. Mon .
"Ground-state properties of small-size nonlinear dynamical lattices". United States.
doi:10.1103/PHYSREVE.75.016212.
```

```
@article{osti_21072276,
```

title = {Ground-state properties of small-size nonlinear dynamical lattices},

author = {Buonsante, P. and Penna, V. and Kevrekidis, P. G. and Vezzani, A.},

abstractNote = {We investigate the ground state of a system of interacting particles in small nonlinear lattices with M{>=}3 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground-state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground-state (modulational) instability appears to be intimately connected with a nonstandard (''double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems.},

doi = {10.1103/PHYSREVE.75.016212},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 1,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}