Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

Abstract

We investigate the systematic generation of higher-order solitons and breathers of the Hirota equa- tion on different backgrounds. The Darboux transfor- mation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher- order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

Publication
Nonlinear Dynamics 89:1637–1649 (2017)
Date
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