State Transition Induced by Self-Steepening and Self Phase-Modulation

doi:10.1088/0256-307X/31/1/010502

Chin. Phys. Lett.

2014, Vol. 31

Issue (1): 010502 DOI: 10.1088/0256-307X/31/1/010502

GENERAL

State Transition Induced by Self-Steepening and Self Phase-Modulation

HE Jing-Song^1,2, XU Shu-Wei³, M. S. Ruderman⁴, R. Erdélyi⁴

¹Department of Mathematics, Ningbo University, Ningbo 315211
²DAMTP, University of Cambridge, Cambridge CB3 0WA, UK
³School of Mathematics, University of Science and Technology of China, Hefei 230026
⁴Solar Physics and Space Plasma Research Centre, University of Sheffield, Sheffield, S3 7RH, UK

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HE Jing-Song, XU Shu-Wei, M. S. Ruderman et al 2014 Chin. Phys. Lett. 31 010502

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Abstract We present a rational solution for a mixed nonlinear Schr?dinger (MNLS) equation. This solution has two free parameters, a and b, representing the contributions of self-steepening and self phase-modulation (SPM) of an associated physical system, respectively. It describes five soliton states: a paired bright-bright soliton, a single soliton, a paired bright-grey soliton, a paired bright-black soliton, and a rogue wave state. We show that the transition among these five states is induced by self-steepening and SPM through tuning the values of a and b. This is a unique and potentially fundamentally important phenomenon in a physical system described by the MNLS equation.

Received: 16 August 2013 Published: 28 January 2014

PACS:	05.45.Yv	(Solitons)
	42.65.Re	(Ultrafast processes; optical pulse generation and pulse compression)
	52.35.Sb	(Solitons; BGK modes)
	02.30.Ik	(Integrable systems)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/31/1/010502 OR https://cpl.iphy.ac.cn/Y2014/V31/I1/010502

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	HE Jing-Song
	XU Shu-Wei
	M. S. Ruderman
	R. Erdélyi

[1] Mio K et al 1976 J. Phys. Soc. Jpn. 41 265
[2] Medvedev M V et al 1997 Phys. Rev. Lett. 78 4934
[3] Laveder D et al 2013 Phys. Lett. A 377 1535
[4] Tzoar N and Jain M 1981 Phys. Rev. A 23 1266
[5] Anderson D and Lisak M 1983 Phys. Rev. A 27 1393
[6] Zabolotskii A A 1987 Phys. Lett. A 124 500
[7] Wadati M et al 1979 J. Phys. Soc. Jpn. 46 1965
[8] Kundu A 1984 J. Math. Phys. 25 3433
[9] Porsezian K et al 2000 Chaos Solitons Fractals 11 2223
[10] Ding Q and Zhu Z N 2002 Phys. Lett. A 295 192
[11] Kundu A 2006 Symmetry, Integrability and Geometry: Methods and Applications 2 078
[12] Kawata T et al 1980 J. Phys. Soc. Jpn. 48 1371
[13] Chowdhury A R et al 1985 Phys. Rev. D 32 3233
[14] Mihalache D et al 1993 Phys. Rev. A 47 3190
[15] Doktorov E V 2002 Eur. Phys. J. B 29 227
[16] Rangwala A A and Rao J A 1990 J. Math. Phys. 31 1126
[17] Wrigh O C 2004 Chaos Solitons Fractals 20 735
[18] Xia T C et al 2005 Chaos Solitons Fractals 26 889
[19] Zhang H Q et al 2012 Phys. Scr. 85 015007
[20] Liu S L and Wang W Z 1993 Phys. Rev. E 48 3054
[21] Li M et al 2010 Phys. Rev. E 81 046606
[22] Golovchenko E A et al 1985 JETP Lett. 42 87
[23] Chen X J and Yan J K 2002 Phys. Rev. E 65 066608
[24] Shchesnovich V S and Doktorov E V 1999 Physica D 129 115
[25] Lashkin V M 2004 Phys. Rev. E 69 016611
[26] He J S et al 2013 Phys. Rev. E 87 052914
[27] Xu S W et al 2011 J. Phys. A: Math. Theor. 44 305203
[28] Xu S W and He J S 2012 J. Math. Phys. 53 063507
[29] Tao Y S and He J S 2012 Phys. Rev. E 85 026601
[30] He J S et al 2012 Phys. Rev. E 86 066603
[31] Ablowitz M J 2011 Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (Cambridge: Cambridge University Press) p 153
[32] Alfvén H 1942 Nature 150 405
[33] Jess D B et al2009 Science 323 1582
[34] Parnell C E and De Moortel I 2012 Phil. Trans. R. Soc. A 370 3217
[35] M Mathioudakis et al 2013 Space Sci. Rev. 175 1
[36] Wedemeyer-B?hm S et al 2012 Nature 486 505
[37] Morton R et al 2012 Nat. Commun. 3 1315
[38] Nakamura A 1981 J. Phys. Soc. Jpn. 50 2469
Nakamura A 1982 J. Phys. Soc. Jpn. 51 19
[39] Sasa N and Satsuma J 1991 J. Phys. Soc. Jpn. 60 409
[40] Li Y S and Han W T 2001 Chin. Ann. Math. B 22 171
[41] Li Z H et al 2000 Phys. Rev. Lett. 84 4096
[42] Kevrekidis P G et al 2003 New J. Phys. 5 64
[43] Choudhuri A and Porsezian K 2012 Opt. Commun. 285 364
[44] Peregrine D H 1983 J. Aust. Math. Soc. Ser. B: Appl. Math. 25 16
[45] He J S et al 2012 J. Phys. Soc. Jpn. 81 033002
[46] Bandelow U and Akhmediev N 2012 Phys. Rev. E 86 026606
[47] Serkin V N et al 2007 Phys. Rev. Lett. 98 074102
[48] Belmonte-Beitia J et al 2007 Phys. Rev. Lett. 98 064102
[49] Belmonte-Beitia J et al 2008 Phys. Rev. Lett. 100 164102
[50] He J S and Li Y S 2011 Stud. Appl. Math. 126 1
[51] Lenells J 2008 Physica D 237 3008
[52] Guo B L et al 2013 Stud. Appl. Math. 130 317
[53] Zhang Y S et al 2013 Commun. Nonlinear Sci. Numer. Simulat. (in press) (also see: arXiv:1304.2579v1)

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