Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation

doi:10.1088/1674-1056/25/1/010507

Abstract

In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schrödinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability (MI) process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov-Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schrödinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton's peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.

Keywords: Kuznetsov-Ma soliton Akhmediev breather

Received: 29 May 2015
Revised: 07 September 2015
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	42.65.Tg	(Optical solitons; nonlinear guided waves)

Fund:

Project supported by the Key Project of Scientific and Technological Research in Hebei Province, China (Grant No. ZD2015133).

Corresponding Authors: Zai-Dong Li
E-mail: lizd2018@live.com

Cite this article:

Zai-Dong Li(李再东), Xuan Wu(吴璇), Qiu-Yan Li(李秋艳), P B He(贺鹏斌) Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation 2016 Chin. Phys. B 25 010507

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Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation

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