On the stability of localized structures in the complex Ginzburg-Landau equation. (English) Zbl 1040.35111
Summary: We study analytically the asymptotic linear stability of fixed-modulus dissipative-dispersive localized solutions of the one-dimensional quintic complex Ginzburg-Landau equation in the region where there exists a coexistence of homogeneous attractors. The linear analysis gives an indication for the existence of pulses with an oscillating modulus.
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35B35 | Stability in context of PDEs |
37K45 | Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems |
Keywords:
asymptotic linear stability; fixed-modulus dissipative-dispersive localized solutions; homogeneous-attractor coexistenceReferences:
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