Spectra of short pulse solutions of the cubic-quintic complex Ginzburg-Landau equation near zero dispersion (Q2822880)

The authors describe computational methods to efficiently determine stationary solutions of the cubic-quintic complex Ginzburg-Landau (CQ-CGL) equation NEWLINE\[NEWLINE iu_z+\frac{D}{2}u_{tt}+\gamma |u|^2u+\nu |u|^4u=i[\delta u+ \beta u_{tt}+\epsilon |u|^2u+\mu |u|^4u] NEWLINE\]NEWLINE 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.