Complex Ginzburg–Landau equations as perturbations of nonlinear Schrödinger equations: A Melnikov approach
✍ Scribed by Gustavo Cruz-Pacheco; C. David Levermore; Benjamin P. Luce
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 163 KB
- Volume
- 197
- Category
- Article
- ISSN
- 0167-2789
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📜 SIMILAR VOLUMES
We describe complex Ginzburg-Landau (CGL) traveling hole solutions as singular perturbations of nonlinear Schrrdinger (NLS) dark solitons. Modulation of the free parameters of the NLS solutions leads to a dynamical system describing the CGL dynamics in the vicinity of a traveling hole solution.
The integrability properties of a perturbed nonlinear Schro à dinger equation are studied using Painleve analysis and Lax|s method[ We distinguish between integrability in the Painleve sense and integrability in the Lax sense[ The solution of the perturbed equation\ with the perturbing term dependin