The essential spectrum of periodically stationary solutions of the complex Ginzburg–Landau equation
| Autor: | Jeremy L. Marzuola, Yuri Latushkin, John Zweck, Christopher K. R. T. Jones |
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| Rok vydání: | 2020 |
| Předmět: |
Breather
010102 general mathematics Mathematical analysis Essential spectrum Term (logic) Differential operator 01 natural sciences Stability (probability) 010101 applied mathematics Mathematics (miscellaneous) Linearization Fiber laser 0101 mathematics Diffusion (business) Nonlinear Sciences::Pattern Formation and Solitons Mathematics |
| Zdroj: | Journal of Evolution Equations. 21:3313-3329 |
| ISSN: | 1424-3202 1424-3199 |
| DOI: | 10.1007/s00028-020-00640-8 |
| Popis: | We establish the existence and regularity properties of a monodromy operator for the linearization of the cubic–quintic complex Ginzburg–Landau equation about a periodically stationary (breather) solution. We derive a formula for the essential spectrum of the monodromy operator in terms of that of the associated asymptotic linear differential operator. This result is obtained using the theory of analytic semigroups under the assumption that the Ginzburg–Landau equation includes a spectral filtering (diffusion) term. We discuss applications to the stability of periodically stationary pulses in ultrafast fiber lasers. |
| Databáze: | OpenAIRE |
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