Elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equationстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a prior restriction is to simplify calculations by means of the use of a few Laurent-series solutions instead of one and the use of the residue theorem. The application of this approach to the quintic complex one-dimensional Ginzburg Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. Restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5, have been found as well. We demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation.