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arXiv · 1204.3028

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

Robert Conte·Tuen-Wai Ng
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Abstract

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).

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Robert Conte, Tuen-Wai Ng. 2012-04-13. Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation. https://doi.org/10.1007/s11232-012-0096-4

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