Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations
Halis Yilmaz
TL;DR
This paper develops a Darboux transformation method to find exact solutions of the Gerdjikov-Ivanov equation, including solitons, breathers, and parabolic solutions, expressed via quasideterminants.
Contribution
It introduces a standard Darboux transformation framework for the GI equation and provides explicit quasideterminant solutions for various wave types.
Findings
Explicit soliton solutions derived
Breather and parabolic solutions obtained
Solution expressions in quasideterminants
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.