Geodesic
Detection and construction of an elliptic solution of the complex cubic–quintic Ginzburg–Landau equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 224-235 Cet article a éte moissonné depuis la source Math-Net.Ru

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In evolution equations for a complex amplitude, the equation for the phase is much more intricate than for the amplitude. Nevertheless, general methods should be applicable to both variables. In the example of the traveling-wave reduction of the complex cubic–quintic Ginzburg–Landau (CGL5) equation, we explain how to overcome the difficulties arising in two methods: (1) the criterion that the sum of residues of an elliptic solution is zero and (2) the construction of a first-order differential equation admitting a given equation as a differential consequence (subequation method).
Mots-clés : elliptic solution, residue criterion
Keywords: subequation method, complex quintic Ginzburg–Landau equation. 
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R. Conte; Tuen-Wai Ng. Detection and construction of an elliptic solution of the complex cubic–quintic Ginzburg–Landau equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 224-235. http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a3/

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