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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.

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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References:

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