Abstract
In the present paper we have obtained and analyzed a family of exact periodic solutions of the nonlinear evolution partial differential convecting fluid equation (CFE) by applying a modification of the bilinear transformation method. This modification is used in view of the circumstance that CFE is a non-integrable nonlinear equation. A detailed consideration has been given to the quite important case of balance between the dispersion and nonlinear effects establishing that this balance changes the structure of the equation itself. The exact periodic solutions of CFE have been also found in the important case when CFE is identical with the Kuramoto–Sivashinsky equation.
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