74 citations · 142 across the 5 of their papers we have counts for
6 papers
Darboux Transformation for the Hirota equation
Halis Yilmaz
The Hirota equation is an integrable higher order nonlinear Schrödinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a sta…
Invariants of hyperbolic Partial Differential Operators
Chris Athorne, Halis Yilmaz
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
Binary Darboux Transformation for the Sasa-Satsuma Equation
Jonathan J. C. Nimmo, Halis Yilmaz
The Sasa-Satsuma equation is an integrable higher-order nonlinear Schrödinger equation. Higher-order and multicomponent generalisations of the nonlinear Schrödinger equation are im…
Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations
Halis Yilmaz
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, solit…
On Darboux transformations for the derivative nonlinear Schrödinger equation
Jonathan J. C. Nimmo, Halis Yilmaz
We consider Darboux transformations for the derivative nonlinear Schrödinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented…
Laplace Invariants for General Hyperbolic Systems
Chris Athorne, Halis Yilmaz
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.