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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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