# Existence of solitons in infinite lattice

## Abstract

We consider necessary conditions for existence of optical solitons in one-dimensional nonlinear periodic layered array. We show analytically that in the array with the cubic-quintic nonlinearity bistable solitons are possible whereas for the Kerr nonlinearity they never exist. We investigate asymptotic behavior of the soliton amplitude at infinity. With help of the asymptotic a numerical algorithm for searching the solitons may be developed so that finding a soliton on finite interval is simultaneously the numerical proof of its existence on infinite interval.

- Authors:

- Department of Electrical Engineering-Physical Electronics, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 20778713

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.73.027601; (c) 2006 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; ALGORITHMS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; SOLITONS

### Citation Formats

```
Gisin, Boris V.
```*Existence of solitons in infinite lattice*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVE.73.0.

```
Gisin, Boris V.
```*Existence of solitons in infinite lattice*. United States. doi:10.1103/PHYSREVE.73.0.

```
Gisin, Boris V. Wed .
"Existence of solitons in infinite lattice". United States.
doi:10.1103/PHYSREVE.73.0.
```

```
@article{osti_20778713,
```

title = {Existence of solitons in infinite lattice},

author = {Gisin, Boris V.},

abstractNote = {We consider necessary conditions for existence of optical solitons in one-dimensional nonlinear periodic layered array. We show analytically that in the array with the cubic-quintic nonlinearity bistable solitons are possible whereas for the Kerr nonlinearity they never exist. We investigate asymptotic behavior of the soliton amplitude at infinity. With help of the asymptotic a numerical algorithm for searching the solitons may be developed so that finding a soliton on finite interval is simultaneously the numerical proof of its existence on infinite interval.},

doi = {10.1103/PHYSREVE.73.0},

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

number = 2,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

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