Generalized Darboux transformation and solitons for the Ablowitz–Ladik equation in an electrical lattice

Abstract

In this paper, the Ablowitz–Ladik equation, which describes an electrical lattice employing the inductors and nonlinear capacitors in a transmission line, is investigated. With respect to the complex field amplitude of the electrical lattice, we construct a generalized Darboux transformation in which the multiple spectral parameters are involved. Expressions of the one-soliton solutions are derived. Soliton velocities, amplitudes and widths are presented. Then, solitons, degenerate solitons and interaction among the soliton and degenerate solitons are investigated. We find that when the multi solitons interact with each other/one another, the corrugated regions are generated in the interaction areas. Interactions among the one soliton and degenerate solitons are shown to be elastic.