Proof of the Absence of Elliptic Solutions of the Cubic Complex Ginzburg-Landau Equation |
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Authors: | S. Yu. Vernov |
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Affiliation: | (1) Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia |
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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. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 161–171, January, 2006. |
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Keywords: | standing wave elliptic function Laurent series residue theorem cubic complex Ginzburg-Landau equation |
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