Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations

Abstract

We study the Gerdjikov-Ivanov (GI) equation and present a standard Darboux transformation for it. The solution is given in terms of quasideterminants. Further, the parabolic, soliton and breather solutions of the GI equation are given as explicit examples.

16 pages, 4 figures

References in corpus (2)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations