Patterns of Dynamics by Pavel Gurevich Juliette Hell Björn Sandstede & Arnd Scheel

Author:Pavel Gurevich, Juliette Hell, Björn Sandstede & Arnd Scheel
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

for some and , belongs to the essential spectrum of . We may rewrite this in complex notation and find the dispersion set

(3.43)

The elements of the dispersion set are

They lie on the vertical line and on infinitely many horizontal lines given for by , see Fig. 8a, b.

Fig. 8.Subsets and of the spectrum for the cubic-quintic Ginzburg-Landau wave equation for with parameters (3.12) (a, b) and two different views of the numerical spectrum on a ball with radius (c, d)

Fig. 9.Eigenfunctions of the cubic-quintic Ginzburg-Landau wave equation for parameters (3.12) belonging to the isolated eigenvalues (a) and (b) and a zoom into the spectrum from Fig. 8c in (c).

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