TL;DR
This paper develops a Darboux transformation method for the Hirota equation, enabling explicit construction of multisoliton and breather solutions for modeling ultrashort light pulse propagation.
Contribution
It introduces a standard Darboux transformation for the Hirota equation and constructs its quasideterminant solutions, advancing solution techniques for this integrable system.
Findings
Explicit multisoliton solutions derived
Breather solutions constructed
Method enhances understanding of ultrashort pulse dynamics
Abstract
The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger 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. The multisoliton and breather solutions of the Hirota equation are given explicitly.
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