Abstract.
In this paper, a two-component (2 + 1) -dimensional long-wave-short-wave (LWSW) system with nonlinearity coefficients, which describes the nonlinear resonance interaction between two short waves and a long wave, is studied. Via the Hirota's bilinear method and Pfaffian, N -order rogue waves for the LWSW system are constructed. Furthermore, correction of the N -order rogue waves is proved directly via the Pfaffian, which is cumbersome or inaccessible in other methods. Results of the first- and second-order rogue waves are presented: 1) For the first-order rogue waves, the two short-wave components are bright, while the long-wave component is dark. The position of maximum amplitude of the rogue wave is analyzed. Evolution process for the first-order rogue wave is also presented and discussed. 2) Choosing different forms of the elements defined in the Pfaffian, we obtain some kinds of the second-order rogue waves with new spatial distributions: when the elements defined in Pfaffian are the same as the first-order rogue waves, we find that the second-order rogue waves for the two short-wave components are split into two first-order rogue waves and the two bumps coexist and interact with each other; when we change the combination of the elements in Pfaffian, we find that the second-order rogue waves for the two short-wave components are split into three and four first-order rogue waves. 3) N -order rogue waves for a general M -component LWSW system are constructed.
Similar content being viewed by others
References
M. Onorato, D. Proment, A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011)
C. Kharif, E. Pelinovsky, A. Slunyaev, Rogue Waves in the Ocean (Springer, Berlin, 2009) 107, 184502 (2011)
W.M. Moslem, P.K. Shukla, B. Eliasson, EPL 96, 25002 (2011)
L. Stenflo, M. Marklund, J. Plasma Phys. 76, 293 (2010)
W.M. Moslem, Phys. Plasmas 18, 032301 (2011)
L. Stenflo, P.K. Shukla, J. Plasma Phys. 75, 841 (2009)
M. Shats, H. Punzmann, H. Xia, Phys. Rev. Lett. 104, 104503 (2010)
D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)
R. Höhmann, U. Kuhl, H.J. Stöckmann, L. Kaplan, E.J. Heller, Phys. Rev. Lett. 104, 093901 (2010)
A. Montina, U. Bortolozzo, S. Residori, F.T. Arecchi, Phys. Rev. Lett. 103, 173901 (2009)
Y.V. Bludov, V.V. Konotop, N. Akhmediev, Phys. Rev. A 80, 033610 (2009)
N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373, 675 (2009)
N. Akhmediev, E. Pelinovsky, Eur. Phys. J. ST 185, 1 (2010)
D.H. Peregrine, J. Austral. Math. Soc. Ser. B 25, 16 (1983)
B. Guo, L. Ling, Q.P. Liu, Phys. Rev. E 85, 026607 (2012)
L. Ling, B. Guo, L.C. Zhao, Phys. Rev. E 89, 041201 (2014)
B. Guo, L. Ling, Q.P. Liu, Stud. Appl. Math. 130, 317 (2013)
Y. Ohta, J. Yang, Proc. R. Soc. A 468, 1716 (2012)
Y. Ohta, J. Yang, J. Phys. A 47, 255201 (2014)
W.P. Zhong, M.R. Belić, T.W. Huang, Phys. Rev. E 85, 026607 (2012)
Shally Loomba, Harleen Kaur, Phys. Rev. E 88, 062903 (2013)
Y. Ohta, J. Yang, Phys. Rev. E 86, 036604 (2012)
Y. Ohta, J. Yang, J. Phys. A 46, 105202 (2013)
A. Ankiewicz, J.M. Soto-Crespo, N. Akhmediev, Phys. Rev. E 81, 046602 (2010)
U. Bandelow, N. Akhmediev, Phys. Rev. E 86, 026606 (2012)
S. Chen, L.Y. Song, Phys. Lett. A 378, 1228 (2014)
W.R. Sun, B. Tian, H.L. Zhen, Y. Sun, Nonlinear Dyn. 81, 725 (2015)
A. Kundu, A. Mukherjee, arXiv:1305.4023 (2013)
A.R. Osborne, M. Onorato, M. Serio, Phys. Lett. A 275, 386 (2000)
M. Onorato, T. Waseda, A. Toffoli, L. Cavaleri, O. Gramstad, P.A.E.M. Janssen, T. Kinoshita, J. Monbaliu, N. Mori, A.R. Osborne, M. Serio, C.T. Stansberg, H. Tamura, K. Trulsen, Phys. Rev. Lett. 102, 114502 (2009)
Bengt Eliasson, P.K. Shukla, Phys. Rev. Lett. 105, 014501 (2010)
A. Kundu, A. Mukherjee, T. Naskar, Proc. R. Soc. A 470, 2164 (2014)
A. Mukherjee, M.S. Janaki, A. Kundu, Phys. Plasmas 22, 072302 (2015)
Y. Ohta, K. Maruno, M. Oikawa, J. Phys. A 40, 7659 (2007)
M. Oikawa, M. Okamura, M. Funakoshi, J. Phys. Soc. Jpn. 58, 4416 (1989)
R.H.J. Grimshaw, Stud. Appl. Math. 56, 241 (1977)
J. Chen, Y. Chen, B.F. Feng, K. Maruno, J. Phys. Soc. Jpn. 84, 034002 (2015)
R. Hirota, Y. Ohta, J. Phys. Soc. Jpn. 60, 789 (1991)
R. Hirota, Phys. Rev. Lett. 27, 1192 (1971)
R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, Cambridge, 2004)
J. Chai, B. Tian, X.Y. Xie, Y. Sun, Commun. Nonlinear Sci. Numer. Simulat. 39, 472 (2016)
J. Chai, B. Tian, W.R. Sun, X.Y. Xie, Comput. Math. Appl. 71, 2060 (2016)
J.W. Yang, Y.T. Gao, Y.J. Feng, C.Q. Su, Solitons and dromion-like structures in an inhomogeneous optical fiber, Nonlinear Dyn. (2016) DOI:10.1007/s11071-016-3083-8
H.M. Yin, B. Tian, J. Chai, X.Y. Wu, W.R. Sun, Appl. Math. Lett. 58, 178 (2016)
H.M. Yin, B. Tian, H.L. Zhen, J. Chai, X.Y. Wu, Mod. Phys. Lett. B 30, 1650306 (2016)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yang, JW., Gao, YT., Sun, YH. et al. Higher-order rogue waves with new spatial distributions for the (2 + 1) -dimensional two-component long-wave-short-wave resonance interaction system. Eur. Phys. J. Plus 131, 416 (2016). https://doi.org/10.1140/epjp/i2016-16416-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2016-16416-8