Bäcklund transformation, superposition formulae and N-soliton solutions for the perturbed Korteweg–de Vries equation

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.

► We have derived BT for the perturbed KdV equation by introducing the auxiliary variable for the first time. ► We have given SF for the the perturbed KdV equation for the first time. ► N-soliton solutions in terms of Wronskian based on BT have been derived.