WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
New Periodic Exact Solutions of the Kuramoto-Sivashinsky Evolution Equation
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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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Keywords: Hirota bilinear operators, Hirota-Matsuno bilinear transformation method, Weierstrass elliptic functions, Jacobi elliptic functions, Jacobi Theta functions, phase modulations of elliptic functions
Pages: 345-352
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #32