This article is cited in 14 papers

Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg–Landau Equation

S. Yu. Vernov

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: We consider the cubic complex Ginzburg–Landau equation. Using Hone's method, based on formal Laurent-series solutions and the residue theorem, we prove the absence of elliptic standing-wave solutions of this equation. This result complements a result by Hone, who proved the nonexistence of elliptic traveling-wave solutions. We show that it is more efficient to apply Hone's method to a system of polynomial differential equations rather than to an equivalent differential equation.

Keywords: standing wave, elliptic function, Laurent series, residue theorem, cubic complex Ginzburg–Landau equation.

DOI: 10.4213/tmf2016

 English version: Theoretical and Mathematical Physics, 2006, 146:1, 131–139

Bibliographic databases:

• 
• 
• 
• 
• 
•