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.

arXiv comment16 pages, 4 figures

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Cited by in corpus (4)

• Binary Darboux Transformation for the Sasa-Satsuma Equation
• On integrable wave interactions and Lax pairs on symmetric spaces
• The long-time asymptotic of the derivative nonlinear Schr$\ddot{o}$dinger equation with step-like initial value
• Darboux Transformation for the Hirota equation