Chin. Phys. Lett.  2017, Vol. 34 Issue (1): 010202    DOI: 10.1088/0256-307X/34/1/010202
Rogue Waves in the (2+1)-Dimensional Nonlinear Schrödinger Equation with a Parity-Time-Symmetric Potential
Yun-Kai Liu, Biao Li**
Ningbo Collaborative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere, and Department of Mathematics, Ningbo University, Ningbo 315211
Cite this article:   
Yun-Kai Liu, Biao Li 2017 Chin. Phys. Lett. 34 010202
Download: PDF(745KB)   PDF(mobile)(728KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract The (2+1)-dimension nonlocal nonlinear Schrödinger (NLS) equation with the self-induced parity-time symmetric potential is introduced, which provides spatially two-dimensional analogues of the nonlocal NLS equation introduced by Ablowitz et al. [Phys. Rev. Lett. 110 (2013) 064105]. General periodic solutions are derived by the bilinear method. These periodic solutions behave as growing and decaying periodic line waves arising from the constant background and decaying back to the constant background again. By taking long wave limits of the obtained periodic solutions, rogue waves are obtained. It is also shown that these line rogue waves arise from the constant background with a line profile and disappear into the constant background again in the $(x,y)$ plane.
Received: 29 August 2016      Published: 29 December 2016
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
  05.45.Yv (Solitons)  
Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11271211, 11275072 and 11435005, the Ningbo Natural Science Foundation under Grant No 2015A610159, the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No xkzw11502, and the K. C. Wong Magna Fund in Ningbo University.
URL:       OR
E-mail this article
E-mail Alert
Articles by authors
Yun-Kai Liu
Biao Li
[1]Bludov Y V, Konotop V V and Akhmediev N 2009 Phys. Rev. A 80 033610
[2]Bludov Y V, Konotop V V and Akhmediev N 2010 Eur. Phys. J. Spec. Top. 185 169
[3]Montina A, Bortolozzo U, Residori S and Arecchi F T 2009 Phys. Rev. Lett. 103 173901
[4]Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054
[5]Höhmann R, Kuhl U, Stöckmann H J, Kaplan L and Heller E J 2010 Phys. Rev. Lett. 104 093901
[6]Kharif C, Pelinovsky E and Slunyaev A 2009 Rogue Waves in the Ocean (Berlin: Springer)
[7]Ganshin A N, Efimov V B, Kolmakov G V, Mezhov-Deglin L P and McClintock P V E 2008 Phys. Rev. Lett. 101 065303
[8]Moslem W M 2011 Phys. Plasmas 18 032301
[9]Bailung H, Sharma S K and Nakamura Y 2011 Phys. Rev. Lett. 107 255005
[10]Yan Z Y 2010 Commun. Theor. Phys. 54 947
[11]Peregrine D H and Aust J 1983 Math. Soc. B 25 16
[12]Dubard P and Matveev V B 2011 Nat. Hazards Earth. Syst. Sci. 11 667
[13]Akhmediev N, Ankiewicz A and Soto-Crespo J M 2009 Phys. Rev. E 80 026601
[14]Dubard P, Gaillard P, Klein C and Matveev V B 2010 Eur. Phys. J. Spec. Top. 185 247
[15]Ankiewicz A, Kedziora D J and Akhmediev N 2011 Phys. Lett. A 375 2782
[16]Guo B, Ling L and Liu Q P 2012 Phys. Rev. E 85 026607
[17]Kedziora D J, Ankiewicz A and Akhmediev N 2011 Phys. Rev. E 84 056611
[18]Ohta Y and Yang J K 2012 Proc. R. Soc. A 468 1716
[19]He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2013 Phys. Rev. E 87 052914
[20]Wang L H, Porsezian K and He J S 2013 Phys. Rev. E 87 053202
[21]Wang X, Li Y Q, Huang F and Chen Y 2015 Commun. Nonlinear Sci. Numer. Simulat. 20 434
[22]Wang X, Cao J L and Chen Y 2015 Phys. Scr. 90 105201
[23]He J S, Xu S W and Porsezian K 2012 Phys. Rev. E 86 066603
[24]Rao J G, Wang L H, Zhang Y and He J S 2015 Commun. Theor. Phys. 64 605
[25]Onorato M, Residori S, Bortolozzo U, Montinad A and Arecchi F T 2013 Phys. Reports 528 47
[26]Ohta Y and Yang J K 2012 Phys. Rev. E 86 036604
[27]Ohta Y and Yang J 2013 J. Phys. A 46 105202
[28]Dudley J M, Dias F, Erkintalo M and Genty G 2014 Nat. Photon. 8 755
[29]Dubard P and Matveev V B 2013 Nonlinearity 26 R93
[30]Chen J C, Chen Y and Feng B F 2015 Phys. Lett. A 379 1510
[31]Mu G and Qin Z Y 2014 Nonlinear Anal. Real World Appl. 18 1
[32]Zhang Y, Sun Y B and Xiang W 2015 Appl. Math. Comput. 263 204
[33]Duan L, Yang Z Y, Liu C and Yang W L 2016 Chin. Phys. Lett. 33 010501
[34]Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110201
[35]Li Y Q, Chen J C, Chen Y and Lou S Y 2014 Chin. Phys. Lett. 31 010201
[36]Ablowitz M J and Musslimani Z H 2013 Phys. Rev. Lett. 110 064105
[37]Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[38]Bender C M, Brody D C and Jones H F 2002 Phys. Rev. Lett. 89 270401
[39]Christodoulides D N and Miri M A 2014 Proc. SPIE 9162 1
[40]El-Ganainy R, Makris K, Christodoulides D N and Musslimani Z H 2007 Opt. Lett. 32 2632
[41]Lévai G and Znojil M 2000 J. Phys. A 33 7165
[42]Berini P and De Leon I 2011 Nat. Photon. 6 16
[43]Makris K, El-Ganainy R, Christodoulides D N and Musslimani Z H 2008 Phys. Rev. Lett. 100 103904
[44]Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N and Peschel U 2012 Nature 488 167
[45]Ruter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[46]Yan Z Y 2015 Appl. Math. Lett. 47 61
[47]Yan Z Y 2016 Appl. Math. Lett. 62 101
[48]Wen X Y, Yan Z Y and Yang Y Q 2016 Chaos 26 063123
[49]Horikis T P and Ablowitz M J 2016 arXiv:1608.00927
[50]Hirota R 2004 The direct method in soliton theory (Cambridge University Press, Cambridge)
[51]Tajiri M and Watanabe Y 1998 Phys. Rev. E 57 3510
[52]Tajiri M and Watanabe Y 1999 Phys. Rev. E 60 2297
[53]Xu Z X and Chow K W 2016 Appl. Math. Lett. 56 72
Related articles from Frontiers Journals
[1] Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 010202
[2] Yu-Han Wu, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction[J]. Chin. Phys. Lett., 2020, 37(4): 010202
[3] Bao Wang, Zhao Zhang, Biao Li. Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schrödinger Equation[J]. Chin. Phys. Lett., 2020, 37(3): 010202
[4] Zhao Zhang, Shu-Xin Yang, Biao Li. Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation[J]. Chin. Phys. Lett., 2019, 36(12): 010202
[5] Zhou-Zheng Kang, Tie-Cheng Xia. Construction of Multi-soliton Solutions of the $N$-Coupled Hirota Equations in an Optical Fiber[J]. Chin. Phys. Lett., 2019, 36(11): 010202
[6] Yong-Shuai Zhang, Jing-Song He. Bound-State Soliton Solutions of the Nonlinear Schrödinger Equation and Their Asymmetric Decompositions[J]. Chin. Phys. Lett., 2019, 36(3): 010202
[7] Ya-Hong Hu, Jun-Chao Chen. Solutions to Nonlocal Integrable Discrete Nonlinear Schrödinger Equations via Reduction[J]. Chin. Phys. Lett., 2018, 35(11): 010202
[8] Wen-Bin He, Xi-Wen Guan. Exact Entanglement Dynamics in Three Interacting Qubits[J]. Chin. Phys. Lett., 2018, 35(11): 010202
[9] Jun Yang, Zuo-Nong Zhu. Higher-Order Rogue Wave Solutions to a Spatial Discrete Hirota Equation[J]. Chin. Phys. Lett., 2018, 35(9): 010202
[10] Zhou-Zheng Kang, Tie-Cheng Xia, Xi Ma. Multi-Soliton Solutions for the Coupled Fokas–Lenells System via Riemann–Hilbert Approach[J]. Chin. Phys. Lett., 2018, 35(7): 010202
[11] Xiang-Shu Liu, Yang Ren, Zhan-Ying Yang, Chong Liu, Wen-Li Yang. Nonlinear Excitation and State Transition of Multi-Peak Solitons[J]. Chin. Phys. Lett., 2018, 35(7): 010202
[12] Zhao-Wen Yan, Mei-Na Zhang Ji-Feng Cui. Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model[J]. Chin. Phys. Lett., 2018, 35(5): 010202
[13] Senyue Lou, Ji Lin. Rogue Waves in Nonintegrable KdV-Type Systems[J]. Chin. Phys. Lett., 2018, 35(5): 010202
[14] Xin Wang, Lei Wang. Soliton, Breather and Rogue Wave Solutions for the Nonlinear Schrödinger Equation Coupled to a Multiple Self-Induced Transparency System[J]. Chin. Phys. Lett., 2018, 35(3): 010202
[15] Yu Wang, Biao Li, Hong-Li An. Dark Sharma–Tasso–Olver Equations and Their Recursion Operators[J]. Chin. Phys. Lett., 2018, 35(1): 010202
Full text