Spectra of short pulse solutions of the cubic-quintic complex Ginzburg-Landau equation near zero dispersion. (English) Zbl 1366.35176
The authors describe computational methods to efficiently determine stationary solutions of the cubic-quintic complex Ginzburg-Landau (CQ-CGL) equation
\[
iu_z+\frac{D}{2}u_{tt}+\gamma |u|^2u+\nu |u|^4u=i[\delta u+ \beta u_{tt}+\epsilon |u|^2u+\mu |u|^4u]
\]
as the parameters in the equation vary, to compute the spectrum of the linearization of the CQCGL equation about these solutions, and to compute the slowly decaying eigenfunctions that correspond to discrete eigenvalues near the continuous spectrum.
Reviewer: Christos Sourdis (Torino)
MSC:
| 35Q56 | Ginzburg-Landau equations |
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
| 65F10 | Iterative numerical methods for linear systems |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B32 | Bifurcations in context of PDEs |
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