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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (7): 74210-074210.doi: 10.1088/1674-1056/22/7/074210

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

陶勇胜^a, 贺劲松^a, K. Porsezian^b

a Department of Mathematics, Ningbo University, Ningbo 315211, China;
b Department of Physics, Pondicherry University, Puducherry 605014, India

收稿日期:2012-09-21 修回日期:2012-11-02 出版日期:2013-06-01 发布日期:2013-06-01
基金资助:
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.

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

Tao Yong-Sheng (陶勇胜)^a, He Jing-Song (贺劲松)^a, K. Porsezian^b

a Department of Mathematics, Ningbo University, Ningbo 315211, China;
b Department of Physics, Pondicherry University, Puducherry 605014, India

Received:2012-09-21 Revised:2012-11-02 Online:2013-06-01 Published:2013-06-01
Contact: He Jing-Song E-mail:hejingsong@nbu.edu.cn;jshe@ustc.edu.cn
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: inhomogeneous nonlinear Schrö, dinger equation, Lax pair, Darboux transformation, soliton

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.

Key words: inhomogeneous nonlinear Schrödinger equation, Lax pair, Darboux transformation, soliton

中图分类号: (Optical solitons; nonlinear guided waves)

42.65.Tg

52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)) 05.45.Yv (Solitons)

陶勇胜, 贺劲松, K. Porsezian. Deformed soliton, breather, and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation[J]. 中国物理B, 2013, 22(7): 74210-074210.

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[J]. Chin. Phys. B, 2013, 22(7): 74210-074210.

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

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

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