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Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg-Landau Equation

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Abstract

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.

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  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

    S. Yu. Vernov

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 161–171, January, 2006.

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Vernov, S.Y. Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg-Landau Equation. Theor Math Phys 146, 131–139 (2006). https://doi.org/10.1007/s11232-006-0013-9

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