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The essential spectrum of periodically-stationary solutions of the complex Ginzburg-Landau equation

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 نشر من قبل Jeremy Marzuola
 تاريخ النشر 2020
  مجال البحث
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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.



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