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

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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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     author = {R. Conte and Tuen-Wai Ng},
     title = {Detection and construction of an~elliptic solution of the~complex cubic--quintic {Ginzburg--Landau} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {224--235},
     publisher = {mathdoc},
     volume = {172},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a3/}
}
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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/