Geodesic
Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg--Landau Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 161-171

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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, residue theorem, cubic complex Ginzburg–Landau equation.
Mots-clés : Laurent series 
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S. Yu. Vernov. Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg--Landau Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 161-171. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a12/