|Autors: Kamenov, O. Y.|
Title: New Periodic Exact Solutions of the Kuramoto-Sivashinsky Evolution Equation
Keywords: Hirota bilinear operators, Hirota-Matsuno bilinear transformation method, Weierstrass elliptic functions, Jacobi elliptic functions, Jacobi Theta functions, phase modulations of elliptic functions
Abstract: In the present paper, three families of exact periodic localized solutions of the popular Kuramoto-Sivashinsky model evolution partial differential equation have been obtained. Similar exact solutions have not been published so far. The exact solutions found are cnoidal, sinusoidal and a solitary-wave one, which were established to be dynamically equivalent. To obtain them a spatial modification of the Hirota-Matsuno bilinear transformation method has been applied. The non-integrability of the evolution equation under consideration generates specific dynamic phenomena – the individual spatial displacements, defined exactly for each separate harmonics in the localized periodic solutions.
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