Proof of the absence of elliptic solutions of the cubic complex Ginzburg-Landau equationстатья
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Аннотация: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.