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Exploding Solitons and Shilnikovs Theorem

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Date

2003

Authors

Akhmediev, Nail
Soto-Crespo, Jose M

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.

Description

Keywords

Keywords: article; elementary particle; evolution; explosion; linear system; mathematics; molecular stability; oscillation; theory Complex Ginzburg-Landau equation; Dissipative solitons

Citation

URI

http://hdl.handle.net/1885/86691

Collections

ANU Research Publications

Source

Physics Letters A

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1016/j.physleta.2003.08.060

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