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

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.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the Ablowitz-Ladik equation that describes an electrical lattice. A generalized Darboux transformation is constructed for the complex field amplitude of the lattice, involving multiple spectral parameters. The expressions of one-soliton solutions are derived and the characteristics of solitons, including velocities, amplitudes, and widths, are presented. The interactions among solitons, degenerate solitons, and a combination of solitons and degenerate solitons are examined. The findings reveal that corrugated regions are generated in the interaction areas of multi-solitons and elastic interactions occur between a single soliton and degenerate solitons.