Densities and fluxes of the conservation laws for the Kuramoto-Sivashinsky equation

Subject Areas : Geometry

M. Jafari ¹ , Y. Alipour Fakhri ² , M. Khadivar ³

1 - Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran
2 - Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran
3 - Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran

Received: 2022-02-04 Accepted : 2022-03-24 Published : 2022-03-25

Keywords: KS equation‎, ‎Conversation laws‎, ‎scaling symmetry‎, ‎homotopy operator,

Abstract :

‎In this paper‎, ‎the main purpose is to calculate the conservation laws of Kuramoto-Sivashinsky equation using‎ the scaling method‎. ‎Linear algebra and calculus of variations are used in this algorithmic method‎. ‎Also the density of the conservation law is obtained by scaling symmetries of the equation and the flux corresponding to the density is calculated using the homotopy operator‎.

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