New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation
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Authors
Longxing Li
- College of Mathematics and Statistics, Qujing Normal University, Qujing, 655000, P. R. China.
Zhengde Dai
- School of Mathematics and Statistics, Yunnan University, Kunming 650091, P. R. China.
Abstract
Exact homoclinic breather wave solution for the coupled Schrödinger -Boussinesq equation is obtained by using homoclinic
test technique. Based on the homoclinic breather wave solution, rational homoclinic breather wave solution is generated by
homoclinic breather limit method, rogue wave in the form of the rational homoclinic solution is derived when the period
of homoclinic breather wave goes to infinite. This is a new way for generating rogue wave which is different from direct
constructing method, Darboux dressing technique and ansätz with complexity of parameter. This result shows the homoclinic
rogue wave can be generated from homoclinic breather wave, and it is useful for explaining some related nonlinear phenomenon.
Share and Cite
ISRP Style
Longxing Li, Zhengde Dai, New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2642--2648
AMA Style
Li Longxing, Dai Zhengde, New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation. J. Nonlinear Sci. Appl. (2017); 10(5):2642--2648
Chicago/Turabian Style
Li, Longxing, Dai, Zhengde. "New homoclinic rogue wave solution for the coupled Schrodinger- Boussinesq equation." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2642--2648
Keywords
- Schrödinger -Boussinesq equation
- Hirota bilinear form
- homoclinic breather limit method
- rogue wave.
MSC
References
-
[1]
M. J. Ablowitz, P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering , London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge (1991)
-
[2]
N. Akhmediev, A. Ankiewicz, J. M. Soto-Crespo, Rogue waves and rational solutions of the nonlinear Schrödinger equation, Phys. Rev. E., 80 (2009), 9 pages.
-
[3]
U. Bandelow, N. Akhmediev, Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa- Satsuma case, Phys. Lett. A., 367 (2012), 1558–1561.
-
[4]
Y. V. Bludov, V. V. Konotop, N. Akhmediev, Matter rogue waves, Phys. Rev. A., 80 (2009), 5 pages.
-
[5]
Y. V. Bludov, V. V. Konotop, N. Akhmediev, Vector rogue waves in binary mixtures of Bose-Einstein condensates, Eur. Phys. J. Spec. Top., 185 (2010), 169–180.
-
[6]
A. R. Chowdhury, B. Dasgupta, N. N. Rao, Painlevé analysis and Backlund transformations for coupled generalized Schrödinger -Boussinesq system, Chaos Solitons Fractals, 9 (1998), 1747–1753.
-
[7]
K. Dysthe, H. E. Krogstad, P. Müller, Oceanic rogue waves, Annual review of fluid mechanics, Annu. Rev. Fluid Mech., Annual Reviews, Palo Alto, CA, 40 (2008), 287–310.
-
[8]
A. N. Ganshin, V. B. Efimov, G. V. Kolmakov, L. P. Mezhov-Deglin, P. V. McClintock, Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium, Phys. Rev. lett., 101 (2008), 4 pages.
-
[9]
Y. Hase, J. Satsuma, An N-soliton solution for the nonlinear Schrödinger equation coupled to the Boussinesq equation, J. Phys. Soc. Japan, 57 (1988), 679–682.
-
[10]
X.-B. Hu, B.-L. Guo, H.-W. Tan, Homoclinic orbits for the coupled Schrödinger -Boussinesq equation and coupled Higgs equation, J. Phys. Soc. Japan, 72 (2003), 189–190.
-
[11]
M.-R. Jiang, Z.-D. Dai, Various heteroclinic solutions for the coupled Schrödinger -Boussinesq equation, Abstr. Appl. Anal., 2013 (2013), 5 pages.
-
[12]
C. Kharif, E. Pelinovsky, A. Slunyaev, Rogue waves in the ocean, Advances in Geophysical and Environmental Mechanics and Mathematics, Springer-Verlag, Berlin (2009)
-
[13]
C.-Z. Li, J.-S. He, K. Porseizan, Rogue waves of the Hirota and the Maxwell-Bloch equations, Phys. Rev. E, 87 (2013), 13 pages.
-
[14]
A. Montina, U. Bortolozzo, S. Residori, F. T. Arecchi, Non-Gaussian statistics and extreme waves in a nonlinear optical cavity, Phys. Rev. Lett., 103 (2009), 4 pages.
-
[15]
G. Mu, Z.-Y. Qin, Rogue waves for the coupled Schrödinger -Boussinesq equation and the coupled Higgs equation, J. Phys. Soc. Japan, 81 (2012), 6 pages.
-
[16]
Y. Ohta, J.-K. Yang, Dynamics of rogue waves in the Davey-Stewartson II equation, J. Phys. A, 46 (2013), 19 pages.
-
[17]
D. H. Peregrine, Water waves, nonlinear Schrödinger equations and their solutions, J. Austral. Math. Soc. Ser. B, 25 (1983), 16–43.
-
[18]
N. N. Rao, P. K. Shukla, Coupled Langmuir and ion-acoustic waves in two-electron temperature plasmas, Phys. Plasmas, 4 (1997), 636–645.
-
[19]
P. Saha, S. Banerjee, A. R. Chowdhury, Normal form analysis and chaotic scenario in a Schrödinger -Boussinesq system, Chaos Solitons Fractals, 14 (2002), 145–153.
-
[20]
N. L. Shatashvili, N. N. Rao, Localized nonlinear structures of intense electromagnetic waves in two-electron-temperature electron-positron-ion plasmas, Phys. Plasmas, 6 (1999), 66–71.
-
[21]
D. R. Solli, C. Ropers, P. Koonath, B. Jalali, Optical rogue waves, Nature, 450 (2007), 1054–1057.
-
[22]
Y.-S. Tao, J.-S. He, Multisolitons, breathers, and rogue waves for the Hirota equation generated by the Darboux transformation, Phys. Rev. E, 85 (2012), 7 pages.
-
[23]
C.-J. Wang, Z.-D. Dai, Various breathers and rogue waves for the coupled long-wave-short-wave system, Adv. Difference Equ., 87 (2014), 10 pages.
-
[24]
C.-J. Wang, Z.-D. Dai, C.-F. Liu, From a breather homoclinic wave to a rogue wave solution for the coupled Schrödinger - Boussinesq equation, Phys. Scripta, 89 (2014), 10 pages.
-
[25]
Z.-Y. Yan, Financial rogue waves, Commun. Theor. Phys., 54 (2010), 947–949.
-
[26]
X.-J. Yang, A new integral transform operator for solving the heat-diffusion problem, Appl. Math. Lett., 64 (2017), 193– 197.
-
[27]
X.-J. Yang, D. Baleanu, Y. Khan, S. T. Mohyud-Din, Local fractional variational iteration method for diffusion and wave equations on Cantor sets, Romanian J. Phys., 59 (2014), 36–48.
-
[28]
X.-J. Yang, F. Gao, A new technology for solving diffusion and heat equations, Therm. Sci., 21 (2017), 133–140.
-
[29]
X.-J. Yang, F. Gao, H. M. Srivastava, Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations, Comput. Math. Appl., 73 (2017), 203–210.
-
[30]
L.-C. Zhao, J. Liu, Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation, Phys. Rev. E., 87 (2013), 8 pages.
-
[31]
W.-P. Zhong, Rogue wave solutions of the generalized one-dimensional Gross-Pitaevskii equation, J. Nonlinear Opt. Phys. Mater., 21 (2012), 9 pages.