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Soliton fusion and fission in a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids. (English) Zbl 1410.76058
Summary: Under investigation in this paper is a generalized variable-coefficient fifth-order Korteweg-de Vries equation, which describes the interaction between a water wave and a floating ice cover or the gravity-capillary waves. Via the Hirota method, Bell-polynomial approach and symbolic computation, bilinear forms, \(N\)-soliton solutions, Bäcklund transformation and Lax pair are derived. Infinitely-many conservation laws are obtained based on the Bell-polynomial-typed Bäcklund transformation. Soliton fusion and fission, and influence of the variable coefficients from the equation are analyzed: Both variable coefficients \(c(t)\) and \(n(t)\) are in direct proportion to the soliton velocities but have no effect on the amplitudes, while another constant coefficient \(\alpha\) can affect the types of the interactions, in the sense of the elastic or inelastic. Elastic-inelastic interactions among the three solitons are presented as well.

MSC:
76D33 Waves for incompressible viscous fluids
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35Q51 Soliton equations
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