References
- M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge: Cambridge University Press, 1991.
- D.S. Agafontsev and V.E. Zakharov, Integrable turbulence and formation of rogue waves, Nonlinearity28 (2015), pp. 2791–2821.
- N. Akhmediev and V.I. Korneev, Modulation instability and periodic solutions of the nonlinear Schrödinger equation, Theor. Math. Phys. 69 (1986), pp. 1089–1093.
- N. Akhmediev, A. Ankiewicz, and M. Taki, Waves that appear from nowhere and disappear without a trace, Phys. Lett. A 373(6) (2009), pp. 675–678.
- Y.V. Bludov, V.V. Konotop, and N. Akhmediev, Vector rogue waves in binary mixtures of Bose-Einstein condensates, Eur. Phys. J-Spec. Top. 185 (2010), pp. 169–180.
- G.W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer, New York, 1989.
- A. Chabchoub and N. Akhmediev, Observation of rogue wave triplets in water waves, Phys. Lett. A377 (2013), Article ID: 2590.
- A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, Super rogue waves: Observation of a higher-order breather in water waves, Phys. Rev. X 2 (2012), Article ID: 011015.
- S. Chen, J.M. Soto-Crespo, F. Baronio, P. Grelu, and D. Mihalache, Rogue-wave bullets in a composite (2+1)D nonlinear medium, Opt. Express 24 (2016), Article ID: 15251.
- B.F. Feng, L.M. Ling, and Z.N. Zhu, Defocusing complex short-pulse equation and its multi-dark-soliton solution, Phys. Rev. E 93(5) (2016), pp. 052227–052227.
- B.L. Guo, L.M. Ling, and Q.P. Liu, Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions, Phys. Rev. E 85 (2012), Article ID: 026607.
- R. Hirota, Direct Methods in Soliton Theory, Cambridge University Press, Cambridge, 2004.
- C. Kharif, E. Pelinovsky, A. Slunyaev, Rogue Waves in the Ocean, Berlin: Springer, 2009.
- E.A. Kuznetsov, Solitons in a parametrically unstable plasma, Akad. Nauk SSSR Dokl. 236 (1977), pp. 575–577.
- M. Lakshmanan, K. Porsezian, and M. Daniel, Effect of discreteness on the continuum limit of the Heisenberg spin chain, Phys. Lett. A 133 (1988), Article ID: 483.
- D.Y. Liu, B. Tian, and X.Y. Xie, Bound-state solutions, Lax pair and conservation laws for the coupled higher-order nonlinear Schrödinger equations in the birefringent or two-mode fiber, Modern Phys. Lett. B 31(12) (2017), Article ID: 1750067.
- Y.C. Ma, The perturbed plane-wave solution of the cubic Schrödinger equation, Stud. Appl. Math. 60 (1979), pp. 43–58.
- V.B. Matveev and M.A. Salle, Darboux transformation and solitons, Springer, Berlin, 1991.
- W.M. Moslem, P.K. Shukla, and B. Eliasson, Surface plasma rogue waves, EPL 96(2) (2011), Article ID: 25002.
- G. Mu, Z.Y. Qin, and R. Grimshaw, Dynamics of rogue waves on a multi-soliton background in a vector nonlinear Schrödinger equation, SIAM J. Appl. Math. 75(1) (2015), pp. 1–20.
- P.J. Olver, Application of Lie group to Differential Equations, Springer, New York, 1993.
- M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F.T. Arecchi, Rogue waves and their generating mechanisms in different physical contexts, Phys. Rep. 528 (2013), Article ID: 47.
- W.Q. Peng, S.F. Tian, and T.T. Zhang, Dynamics of breather waves and higher-order rogue waves in a coupled nonlinear Schrödinger equation, EPL 123(5) (2018), Article ID: 50005.
- W.Q. Peng, S.F. Tian, and T.T. Zhang, Dynamics of the soliton waves, breather waves, and rogue waves to the cylindrical kadomtsev-petviashvili equation in pair-ionelectron plasma, Phys. Fluids 31 (2019), Article ID: 102107.
- K. Porsezian, M. Daniel, and M. Lakshmanan, On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain, J. Math. Phys. 33 (1992), Article ID: 1807.
- D.R. Solli, C. Ropers, and P. Koonath, Optical rogue waves, Nature 450(7172) (2007), pp. 1054–1057.
- W.R. Sun, D.Y. Liu, and X.Y. Xie, Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers, Chaos 27 (2017), Article ID: 043114.
- S.F. Tian, Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method, J. Differ. Equ. 262(1) (2017), pp. 506–558.
- S.F. Tian, Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval, Commun. Pure Appl. Anal. 17(3) (2018), pp. 923–957.
- S.F. Tian, Infinite propagation speed of a weakly dissipative modified two-component Dullin-Gottwald-Holm system, Appl. Math. Lett. 89 (2019), pp. 1–7.
- X.B. Wang and B. Han, The Kundu-nonlinear Schrödinger equation: Breathers, rogue waves and their dynamics, J. Phys. Soc. Jpn. 89(1) (2020), Article ID: 014001.
- L.H. Wang, K. Porsezian, and J.S. He, Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation, Phys. Rev. E 87 (2013), Article ID: 053202.
- L. Wang, J.H. Zhang, Z.Q. Wang, C. Liu, M. Li, F.H. Qi, and R. Guo, Breather-to-soliton transitions, nonlinear wave interactions, and modulational instability in a higher-order generalized nonlinear Schrödinger equation, Phys. Rev. E 93 (2016), Article ID: 012214.
- X.Y. Wen, Z.Y. Yan, and B.A. Malomed, Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability, Chaos 26 (2016), Article ID: 123110.
- X.-Y. Wu, B. Tian, L. Liu, and Y. Sun, Rogue waves for a variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics, Comput. Math. Appl. 76 (2018), pp. 215–223.
- L. Xu, D.S. Wang, X.Y. Wen, Y.L. Jiang, Exotic localized vector waves in a two-component nonlinear wave system, J. Nonlinear Sci. 30 (2020), pp. 537–564.
- X.W. Yan, S.F. Tian, M.J. Dong, and T.T. Zhang, Rogue waves and their dynamics on bright-dark soliton background of the coupled higher order nonlinear Schrödinger equation, J. Phys. Soc. Jpn.88(7) (2019), Article ID: 074004.
- Z.P. Yang, W.P. Zhong, and M. Belić, 2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients, Laser Phys. 25 (2015), Article ID: 085402.
- L.D. Zhang, S.F. Tian, W.Q. Peng, T.-T. Zhang, and X.-J. Yan, The dynamics of lump, lumpoff and rogue wave solutions of (2+1)-dimensional Hirota-Satsuma-Ito equations, East Asian J. Appl. Math.10(2) (2020), pp. 243–255.