Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

doi:10.1088/1674-1056/23/3/030501

中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30501-030501.doi: 10.1088/1674-1056/23/3/030501

Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

佑六云^a, 李画眉^a, 何俊荣^{a b}

a Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
b Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2013-07-01 修回日期:2013-09-10 出版日期:2014-03-15 发布日期:2014-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11175158 and 11374266) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY12A04001).

Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

You Lu-Yun (佑六云)^a, Li Hua-Mei (李画眉)^a, He Jun-Rong (何俊荣)^{a b}

a Department of Physics, Zhejiang Normal University, Jinhua 321004, China;
b Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2013-07-01 Revised:2013-09-10 Online:2014-03-15 Published:2014-03-15
Contact: Li Hua-Mei E-mail:lihuamei@zjnu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11175158 and 11374266) and the Natural Science Foundation of Zhejiang Province, China (Grant No. LY12A04001).

摘要/Abstract

摘要： We investigate the explicit novel localized nonlinear matter waves of the cubic-quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and the harmonic-lattice potential using a modified similarity transformation. We also find that when the modulus of the Jacobian elliptic function in the limit closes to 1, the shapes of the breathing solitons may exhibit some interesting features, i.e., one breathing soliton dividing into two in the ground state. The stability of the exact solutions is investigated numerically such that some stable breathing soliton solutions are found.

关键词: breathing soliton, cubic-quintic nonlinearity, harmonic-lattice potential

Abstract: We investigate the explicit novel localized nonlinear matter waves of the cubic-quintic nonlinear Schrödinger equation with spatiotemporal modulation of the nonlinearities and the harmonic-lattice potential using a modified similarity transformation. We also find that when the modulus of the Jacobian elliptic function in the limit closes to 1, the shapes of the breathing solitons may exhibit some interesting features, i.e., one breathing soliton dividing into two in the ground state. The stability of the exact solutions is investigated numerically such that some stable breathing soliton solutions are found.

Key words: breathing soliton, cubic-quintic nonlinearity, harmonic-lattice potential

中图分类号: (Solitons)

05.45.Yv

03.75.Lm (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations) 42.65.Tg (Optical solitons; nonlinear guided waves)

佑六云, 李画眉, 何俊荣. Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential[J]. 中国物理B, 2014, 23(3): 30501-030501.

You Lu-Yun (佑六云), Li Hua-Mei (李画眉), He Jun-Rong (何俊荣). Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential[J]. Chin. Phys. B, 2014, 23(3): 30501-030501.

参考文献 34

[1]	Inouye S, Andrews M R, Stenger J, Miesner H J, Stamper-Kurn D M and Ketterle W 1998 Nature 392 151
[2]	Pitaevskii L P and Stringari S 2003 Bose–Einstein Condensation (Oxford: Oxford University Press)
[3]	Mayteevarunyoo T and Malomed B A 2006 Phys. Rev. A 74 033616
[4]	Poletti D, Alexander T J, Ostrovskaya E A, Li B and Kivshar Y S 2008 Phys. Rev. Lett. 101 150403
[5]	Theocharis G, Frantzeskakis D J, Carretero-González R, Kevrekidis P G and Malomed B A 2005 Phys. Rev. E 71 017602
[6]	Wang J D, Ji H and Liu P S 2013 Chin. Phys. B 22 044207
[7]	Tie L and Xue J K 2011 Chin. Phys. B 20 120311
[8]	Choi D I and Niu Q 1999 Phys. Rev. Lett. 82 2022
[9]	Cristiani M, Morsch O, Muller J H, Ciampini D and Arimondo E 2002 Phys. Rev. A 65 063612
[10]	Jona-Lasinio M, Morsch O, Cristiani M, Malossi N, Müller J H, Courtade E, Anderlini M and Arimondo E 2003 Phys. Rev. Lett. 91 230406
[11]	Jona-Lasinio M, Morsch O, Cristiani M, Malossi N, Müller J H, Courtade E, Anderlini M and Arimondo E 2004 Phys. Rev. Lett. 93 119903
[12]	Staliunas K, Herrero R and de Valcárcel G J 2006 Phys. Rev. E 73 065603
[13]	Staliunas K, Herrero R and de Valcárcel G J 2007 Phys. Rev. A 75 011604
[14]	Lignier H, Sias C, Ciampini D, Singh Y, Zenesini A, Morsch O and Arimondo E 2007 Phys. Rev. Lett. 99 220403
[15]	Roberts J L, Claussen N R, Burke J P, Greene C H, Cornell E A and Wieman C E 1998 Phys. Rev. Lett. 81 5109
[16]	Theis M, Thalhammer G, Winkler K, Hellwig M, Ruff G, Grimm R and Denschlag J H 2004 Phys. Rev. Lett. 93 123001
[17]	Schneider P I and Saenz A 2013 Phys. Rev. A 87 052712
[18]	Zhang R, Sapiro R E, Mhaskar R R and Raithel G 2008 Phys. Rev. A 78 053607
[19]	Hawk B N and Nathan K J 2007 Phys. Rev. E 75 036214
[20]	Plata J 2004 Phys. Rev. A 69 033604
[21]	He J R and Li H M 2013 Chin. Phys. B 22 040310
[22]	Ott H, de Mirandes E, Ferlaino F, Roati G, Türck V, Modugno G and Inguscio M 2004 Phys. Rev. Lett. 93 120407
[23]	Li Z W, Ma X M, Pang H and Li F S 2011 J. Phys.: Condens. Matter 23 255701
[24]	Eiermann B, Anker T, Albiez M, Taglieber M, Treutlein P, Marzlin K P and Oberthaler M K 2004 Phys. Rev. Lett. 92 230401
[25]	Blakie P B, Bezett A and Buonsante P J 2007 Phys. Rev. A 75 063609
[26]	Morsch O and Oberthaler M 2006 Rev. Mod. Phys. 78 179
[27]	Wu L, Li Lu, Zhang J F, Mihalache D, Malomed B A and Liu W M 2010 Phys. Rev. A 81 061805
[28]	Zhong W P, Belić M R and Xia Y Z 2011 Phys. Rev. E 83 036603
[29]	Tian Q, Wu L, Zhang J F, Malomed B A, Mihalache D and Liu W M 2011 Phys. Rev. E 83 016602
[30]	Li Z J, Hai W H and Deng Y 2013 Chin. Phys. B 22 090505
[31]	Wang J D, Ji H and Liu P S 2013 Chin. Phys. B 22 044207
[32]	Belmonte-Beitia J, Pérez-García V M, Vekslerchik V and Konotop V V 2008 Phys. Rev. Lett. 100 164102
[33]	Hawkins R M and Lidsey J E 2002 Phys. Rev. D 66 023523
[34]	Tang X Y and Shukla P K 2007 Phys. Rev. A 76 013612

Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

Exact breathing soliton solutions in combined time-dependent harmonic-lattice potential

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