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Bäcklund transformation, superposition formulae and \(N\)-soliton solutions for the perturbed Korteweg-de Vries equation. (English) Zbl 1252.35243
Summary: With symbolic computation, under investigation in this paper is the perturbed Korteweg-de Vries equation for the nonlocal solitary waves and arrays of wave crests. Via the Hirota method, the bilinear form, Bäcklund transformation and superposition formulae are obtained. \(N\)-soliton solutions in terms of the Wronskian are constructed. Asymptotic analysis is used to analyze the collision dynamics, and figures are plotted to illustrate the influence of the perturbation. We find that the perturbation affects the propagation velocities of the solitons, but does not affect the amplitudes and widths of the solitons. Besides, the solitonic collisions turn out to be elastic.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35C08 Soliton solutions
68W30 Symbolic computation and algebraic computation
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