### Abstract

The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.

Original language | English (US) |
---|---|

Pages (from-to) | 63-85 |

Number of pages | 23 |

Journal | Journal of Mathematical Physics |

Volume | 29 |

Issue number | 1 |

State | Published - 1988 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*29*(1), 63-85.

**Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity : Analysis.** / Adachihara, H.; McLaughlin, D. W.; Moloney, Jerome V; Newell, Alan C.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 29, no. 1, pp. 63-85.

}

TY - JOUR

T1 - Solitary waves as fixed points of infinite-dimensional maps for an optical bistable ring cavity

T2 - Analysis

AU - Adachihara, H.

AU - McLaughlin, D. W.

AU - Moloney, Jerome V

AU - Newell, Alan C

PY - 1988

Y1 - 1988

N2 - The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.

AB - The transverse behavior of a laser beam propagating through a bistable optical cavity is investigated analytically and numerically. Numerical experiments that study the (one-dimensional) transverse structure of the steady state profile are described. Mathematical descriptions of (i) an infinite-dimensional map that models the situation, (ii) the solitary waves that represent the transverse steady state structures, (iii) a projection formalism that reduces the infinite-dimensional map to a finite-dimensional one, and (iv) the theoretical analysis of this reduced map are presented in detail. The accuracy of this theoretical analysis is established by comparing its predictions to numerical observations.

UR - http://www.scopus.com/inward/record.url?scp=0011361311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011361311&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0011361311

VL - 29

SP - 63

EP - 85

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

ER -