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Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation. (English) Zbl 1384.35119
Summary: Under investigation in this paper is a coupled nonlinear Schrödinger (NLS) equation, which describes nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order. Based on the Lax pair of the coupled NLS equation, we construct the determinant representation of the \(N\)-fold Darboux transformation(DT). Furthermore, by using the obtained \(N\)-fold DT, we obtain its higher-order soliton, breather and rogue wave solutions. Finally, the dynamic characteristics of these solutions are discussed.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
76B25 Solitary waves for incompressible inviscid fluids
78A60 Lasers, masers, optical bistability, nonlinear optics
35C08 Soliton solutions
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[1] Fokas, A. S., Physica D, 87, 145-150, (1995)
[2] Lenells, L., Stud. Appl. Math., 123, 215-232, (2009)
[3] Lenells, L.; Fokas, A. S., Nonlinearity, 22, 11-27, (2009)
[4] Akhmediev, N.; Soto-Crespo, J. M.; Ankiewicz, A., Phys. Lett. A, 373, 2137-2145, (2009)
[5] Müller, P.; Garrett, C. H.; Osborne, A., Oceanography, 18, 66, (2005)
[6] Kharif, C.; Pelinovsky, E.; Slunyaev, A., Rogue Waves in the Ocean, (2009), Springer New York · Zbl 1230.86001
[7] Solli, D. R.; Ropers, C.; Koonath, P.; Jalali, B., Nature, 450, 1054, (2007)
[8] Yeom, D.-II.; Eggleton, B., Nature, 450, 953, (2007)
[9] Kibler, B.; Fatome, J.; Finot, C.; Millot, G.; Dias, F.; Genty, G.; Akhmediev, N.; Dudley, J. M., Nat. Phys., 6, 790, (2010)
[10] Hirota, R., The Direct Method in Soliton Theory, (2004), Cambridge University Press Cambridge, UK
[11] Vekslerchik, V. E.; Wang, X. B.; Tian, S. F.; Yan, H.; Zhang, T. T.; Feng, L. L.; Tian, S. F.; Wang, X. B.; Zhang, T. T., Nonlinearity, Comput. Math. Appl., Appl. Math. Lett., 65, 90, (2017)
[12] Ohta, B. Y.; Yang, J. K., Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 468, 1716-1740, (2012)
[13] Ablowitz, M. J., Nonlinear dispersive waves, (Cambridge Texts Appl. Math, (2011), CUP Cambridge) · Zbl 1232.35002
[14] Chen, J. C.; Chen, Y.; Feng, B. F.; Maruno, K., Phys. Lett. A, 379, 1510, (2015)
[15] Guo, B. L.; Ling, L. M., Chin. Phys. Lett., 28, 110202, (2011)
[16] Meschede, D.; Steglich, F.; Felsch, W.; Maletta, H.; Zinn, W., Phys. Rev. Lett., 109, 044102, (2012)
[17] Yan, Z. Y.; Wang, X.; Tian, S.; Qin, C.; Zhang, T., Phys. Lett. A, Appl. Math. Lett., 72, 58, (2017)
[18] Ma, W. X.; You, Y.; Ma, W. X.; Abdeljabbar, A., Trans. Amer. Math. Soc., Appl. Math. Lett., 12, 1500, (2012)
[19] Zhao, L. C.; Li, S. C.; Ling, L. M., Phys. Rev. E, 89, 023210, (2014)
[20] Tian, S. F.; Tian, S. F., J. Differential Equations, Proc. R. Soc. Lond. A, 472, 20160588, (2016)
[21] Matsuno, Y.; Wang, X. B.; Tian, S. F.; Qin, C. Y.; Zhang, T. T.; Tu, J. M.; Tian, S. F.; Xu, M. J.; Zhang, T. T., J. Phys. A, Europhys. Lett., Appl. Math. Comput., 275, 1, 345, (2016)
[22] Matveev, V. B.; Smirnov, A. O., Theoret. Math. Phys., 186, 2, 156-182, (2016)
[23] Wang, L.; Zhang, J. H.; Wang, Z. Q.; Liu, C.; Li, M.; Qi, F. H.; Guo, R.; Wang, L.; Zhang, J. H.; Liu, C.; Li, M.; Qi, F. H., Phys. Rev. E, Phys. Rev. E, 93, 062217, (2016)
[24] Guo, R.; Hao, H.; Zhao, H.; Zhao, X.; Hao, H., Ann. Phys., Appl. Math. Lett., 61, 8, (2016)
[25] Zhang, J. H.; Wang, L.; Liu, Chong; Wang, L.; Zhu, Y.; Qi, F.; Li, M.; Guo, R.; Wang, L.; Li, X.; Qi, F.; Zhang, L., Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., Chaos, Ann. Phys., 359, 97, (2015)
[26] Cai, L.; Wang, X.; Wang, L.; Li, M.; Liu, Y.; Shi, Y.; Wang, L.; Wang, Z.; Sun, W.; Shi, Y.; Li, M.; Xu, M.; Wang, L.; Jiang, D.; Qi, F.; Shi, Y.; Zhao, Y., Nonlinear Dynam., Commun. Nonlinear Sci. Numer. Simulat., Commun. Nonlinear Sci. Numer. Simulat., 42, 502, (2017)
[27] Tian, S. F.; Zhang, H. Q.; Wang, X. B.; Tian, S. F.; Qin, C. Y.; Zhang, T. T.; Tian, S. F., Stud. Appl. Math., Appl. Math. Lett., J. Phys. A: Math. Theor., 50, 39, 395204, (2017)
[28] Wazwaz, A. M.; Wazwaz, A. M., Appl. Math. Lett., Appl. Math. Comput., 219, 9057, (2013)
[29] Wang, D. S.; Wei, X. Q.; Wang, D. S.; Yin, Y. B., Appl. Math. Lett., Comput. Math. Appl., 71, 748, (2016)
[30] Tian, S. F.; Zhang, H. Q.; Tian, S. F.; Zhang, H. Q.; Tian, S.; Zhang, Y.; Feng, B.; Zhang, H., J. Phys. A, J. Math. Anal. Appl, Chinese Ann. of Math., Series B, 36, 4, 543, (2015)
[31] Xu, M. J.; Tian, S. F.; Tu, J. M.; Zhang, T. T.; Tu, J. M.; Tian, S. F.; Xu, M. J.; Ma, P. L.; Zhang, T. T., Nonlinear Anal, Comput. & Math. Appl., 72, 2486, (2016)
[32] Tu, J. M.; Tian, S. F.; Xu, M. J.; Zhang, T. T.; Wang, X. B.; Tian, S. F.; Xu, M. J.; Zhang, T. T.; Ma, P.; Tian, S.; Zhang, T., Taiwanese J. Math., Appl. Math. Comput., Appl. Math. Lett., 50, 146, (2015)
[33] Geng, X. G.; Lv, X. Y., Nonlinear Dyn, 69, 1621-1630, (2012)
[34] He, J. S.; Xu, S. W., J. Phys. Soc. Japan, 81, 124007, (2012)
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