The traveling wave solutions of the perturbed nonlinear Schrödinger equation and the cubic–quintic Ginzburg Landau equation using the modified -expansion method
✍ Scribed by A.R. Shehata
- Book ID
- 108051770
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 226 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0096-3003
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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.
Singularity Theory is used to comprehensively investigate the bifurcations of the steady states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy condit