Deformed soliton, breather, and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation

doi:10.1088/1674-1056/22/7/074210

Abstract We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schrödinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schrödinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schrödinger equation under a suitable parametric condition.

Keywords: inhomogeneous nonlinear Schrödinger equation Lax pair Darboux transformation soliton

Received: 21 September 2012
Revised: 02 November 2012
Accepted manuscript online:

PACS:	42.65.Tg	(Optical solitons; nonlinear guided waves)
	52.35.Mw	(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))
	05.45.Yv	(Solitons)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10971109), K. C. Wong Magna Fund in Ningbo University, China, the Natural Science Foundation of 383 Ningbo, China (Grant No. 2011A610179), and the DST, DAE-BRNS, UGC, CSIR, India.

Corresponding Authors: He Jing-Song
E-mail: hejingsong@nbu.edu.cn;jshe@ustc.edu.cn

Cite this article:

Tao Yong-Sheng (陶勇胜), He Jing-Song (贺劲松), K. Porsezian Deformed soliton, breather, and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation 2013 Chin. Phys. B 22 074210

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Deformed soliton, breather, and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation

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