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All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 4 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 4
Number of page(s) 15
DOI https://doi.org/10.1051/mmnp/2022006
Published online 17 February 2022
  1. N. Akhmediev, A. Ankiewicz and M. Taki, Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373 (2009) 675–678. [CrossRef] [Google Scholar]
  2. N. Akhmediev and V.I. Korneev, Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 69 (1986) 1089–1093. [CrossRef] [Google Scholar]
  3. Y.V. Bludov, V.V. Konotop and N. Akhmediev, Matter rogue waves. Phys. Rev. A 80 (2009) 033610. [CrossRef] [Google Scholar]
  4. A. Degasperis and S. Lombardo, Multicomponent integrable wave equations: I. Darboux-dressing transformation. J. Phys. A: Math. Theor. 40 (2007) 961–977. [CrossRef] [Google Scholar]
  5. A. Degasperis and S. Lombardo, Multicomponent integrable wave equations: II. Soliton solutions. J. Phys. A: Math. Theor. 42 (2009) 2467–2480. [Google Scholar]
  6. K. Dysthe, H.E. Krogstad and P. Müller, Oceanic rogue waves. Annu. Rev. Fluid Mech. 40 (2008) 287–310. [CrossRef] [Google Scholar]
  7. H.A. Erbay, Nonlinear transverse waves in a generalized elastic solid and the complex modified Korteweg-de Vries equation. Phys. Scr. 58 (1998) 9–14. [CrossRef] [Google Scholar]
  8. X.G. Geng, Y.Y. Zhai and H.H. Dai, Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy. Adv. Math. 263 (2014) 123–153. [CrossRef] [MathSciNet] [Google Scholar]
  9. B.L. Guo, L.M. Ling, Q.P. Liu and C.F. Wu, Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions. Phys. Rev. E 85 (2012) 026607. [CrossRef] [PubMed] [Google Scholar]
  10. J.S. He, L.H. Wang, L.J. Li, K. Porsezian and R. Erdélyi, Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation. Phys. Rev. E 89 (2014) 062917. [CrossRef] [PubMed] [Google Scholar]
  11. A.H. Khater, O.H. El-Kalaawy and D.K. Callebaut, Bäcklund transformations and exact solutions for Alfvén solitons in a relativistic electron-positron plasma. Phys. Scr. 58 (1988) 545. [CrossRef] [Google Scholar]
  12. B. Kibler, J. Fatome, C. Finot, G. Millot and F. Dias, The Peregrine soliton in nonlinear fibre optics. Nat. Phys. 6 (2010) 790. [CrossRef] [Google Scholar]
  13. E.A. Kuznetsov, Solitons in a parametrically unstable plasma. Akad. Nauk SSSR Dokl. 236 (1977) 575–577. [Google Scholar]
  14. H. Leblond, P. Grelu and D. Mihalache, Models for supercontinuum generation beyond the slowly-varying-envelope approximation. Phys. Rev. A 90 (2014) 053816. [CrossRef] [Google Scholar]
  15. L.M. Ling, B.L. Guo and L.C. Zhao, High-order rogue waves in vector nonlinear Schrödinger equations. Phys. Rev. E 89 (2014) 041201. [CrossRef] [PubMed] [Google Scholar]
  16. K.E. Lonngren, Ion acoustic soliton experiments in a plasma. Opt. Quant. Electron. 30 (1998) 615. [CrossRef] [Google Scholar]
  17. Y. Lou, Y. Zhang and R.S. Ye, Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov-Ivanov equation. Wave Motion 106 (2021) 102795. [CrossRef] [Google Scholar]
  18. Y. Lou, Y. Zhang, R.S. Ye and M. Li, Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation. Appl. Math. Comput. 409 (2021) 126417. [Google Scholar]
  19. W.X. Ma, Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system. J. Geom. Phys. 132 (2018) 45–54. [CrossRef] [MathSciNet] [Google Scholar]
  20. G. Mu, Z.Y. Qin and R. Grimshaw, Dynamics of rogue waves on a multisoliton background in a vector nonlinear Schrödinger equation. SIAM.J. Appl. Math. 75 (2015) 1–20. [CrossRef] [MathSciNet] [Google Scholar]
  21. N.V. Priya, M. Senthilvelan and M. Lakshmanan, Akhmediev breathers, Ma solitons, and general breathers from rogue waves: a case study in the Manakov system. Phys. Rev. E 88 (2013) 022918. [CrossRef] [PubMed] [Google Scholar]
  22. D.R. Solli, C. Ropers, P. Koonath et al., Optical rogue waves. Nature 450 (2007) 1054–1057. [CrossRef] [PubMed] [Google Scholar]
  23. X. Wang, Y. Li and Y. Chen, Generalized Darboux transformation and localized waves in coupled Hirota equations. Wave Motion 51 (2014) 1149–1160. [CrossRef] [MathSciNet] [Google Scholar]
  24. R. Wang, Y. Zhang, X.T. Chen and R.S. Ye, The rational and semi-rational solutions to the Hirota-Maccari system. Nonlinear Dyn. 100 (2020) 2767–2778. [CrossRef] [Google Scholar]
  25. T. Xu and G.L. He, Higher-order interactional solutions and rogue wave pairs for the coupled Lakshmanan-Porsezian-Daniel equations. Nonlinear Dyn. 98 (2019) 1731–1744. [CrossRef] [Google Scholar]
  26. T. Xu and G.L. He, The coupled derivative nonlinear Schrödinger equation: conservation laws, modulation instability and semirational solutions. Nonlinear Dyn. 100 (2020) 2823–2837. [CrossRef] [Google Scholar]
  27. Z.Y. Yan, Vector financial rogue waves. Phys. Lett. A 375 (2011) 4274–4279. [CrossRef] [Google Scholar]
  28. R.S. Ye, Y. Zhang, Q.Y. Zhang and X.T. Chen, Vector rational and semi-rational rogue wave solutions in the coupled complex modified Korteweg-de Vries equations. Wave Motion 92 (2019) 102425. [Google Scholar]
  29. Y.Y. Zhai, T. Ji and X.G. Geng, Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber. Appl. Math. Comput. 411 (2021) 126551. [Google Scholar]
  30. Y. Zhang, R.S. Ye and W.X. Ma, Binary Darboux transformation and soliton solutions for the coupled complex modified Korteweg-de Vries equations. Math. Meth. Appl. Sci. 43 (2019) 613–627. [Google Scholar]
  31. Y. Zhang, J.W. Yang, K.W. Chow et al., Solitons, breathers and rogue waves for the coupled Fokas-Lenells system via Darboux transformation. Nonlinear Anal. RWA 33 (2017) 237–252. [CrossRef] [Google Scholar]

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