Journal of Mathematical Physics, Analysis, Geometry
2022, vol. 18, No 1, pp. 136-152   https://doi.org/10.15407/mag18.01.136     ( to contents , go back )
https://doi.org/10.15407/mag18.01.136

Darboux Transformation for the Hirota Equation

Halis Yilmaz

School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
Department of Mathematics, Mimar Sinan Fine Arts University, Istanbul, Turkey
Department of Mathematics, University of Dicle, 21280 Diyarbakir, Turkey
E-mail: Halis.Yilmaz@glasgow.ac.uk,halisyilmaz@dicle.edu.tr

Received October 13, 2020, revised February 22, 2021.

Abstract

The Hirota equation is an integrable higher order nonlinear Schrodinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions. As examples, the multi-soliton, breather and rogue wave solutions of the Hirota equation are given explicitly.

Mathematics Subject Classification 2010: 35C08, 35Q55, 37K10
Key words: Hirota equation, Darboux transformation, quasideterminant solutions, multisoliton solutions, breather solutions, rogue wave solutions

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