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Analytic study on the Sawada-Kotera equation with a nonvanishing boundary condition in fluids. (English) Zbl 1311.35264
Summary: Under investigation in this paper is the Sawada-Kotera equation with a nonvanishing boundary condition, which describes the evolution of steeper waves of shorter wavelength than those described by the Korteweg-de Vries equation does. With the binary-Bell-polynomial, Hirota method and symbolic computation, the bilinear form and \(N\)-soliton solutions for this model are derived. Meanwhile, propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis. Via Bell-polynomial approach, the Bäcklund transformation is constructed in both the binary-Bell-polynomial and bilinear forms. Based on the binary-Bell-polynomial-type Bäcklund transformation, we obtain the Lax pair and conservation laws associated.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
76B25 Solitary waves for incompressible inviscid fluids
35-04 Software, source code, etc. for problems pertaining to partial differential equations
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