This article is cited in 4 papers

Detection and construction of an elliptic solution of the complex cubic–quintic Ginzburg–Landau equation

R. Conte^ab, Tuen-Wai Ng<sup>b

a</sup> LRC MESO, Centre de mathématiques et de leurs applications et CEA-DAM, École normale supérieure de Cachan, Cachan, France
^b Department of Mathematics, Faculty of Science, The University of Hong Kong, Hong Kong

Abstract: 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).

Keywords: elliptic solution, residue criterion, subequation method, complex quintic Ginzburg–Landau equation.

DOI: 10.4213/tmf6953

 English version: Theoretical and Mathematical Physics, 2012, 172:2, 1073–1084

Bibliographic databases:

• 
• 
• 
• 
• 
•