Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Reviews in mathematical modelling
Article Number 67
Number of page(s) 14
DOI https://doi.org/10.1051/mmnp/2020029
Published online 03 December 2020
  1. H. Bateman, Some recent researches on the motion of fluids. Mon. Weather Rev. 43 (1915) 163–170. [Google Scholar]
  2. J.M. Burgers, A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1 (1948) 171–199. [Google Scholar]
  3. F. Calogero and A. Degasperis, Spectral transform and solitons. North-Holland, Amsterdam (1982). [Google Scholar]
  4. J.C. Chen, Y. Chen, B.F. Feng and K.I. Maruno, Multi-dark soliton solutions of the twodimensional multi-component yajima-oikawa systems. J. Phys. Soc. Jpn. 84 (2015) 034002. [Google Scholar]
  5. S.-S. Chen, B. Tian, Y. Sun and C.-R. Zhang, Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently Coupled Nonlinear Schródinger Equations in Nonlinear Optics. Ann. Phys. 531 (2019) 1900011. [Google Scholar]
  6. Z. Du, B. Tian, H.-P. Chai and X.-H. Zhao, Dark-bright semi-rational solitons and breathers for a higher-order coupled nonlinear Schródinger system in an optical fiber. Appl. Math. Lett. 102 (2020) 106110. [Google Scholar]
  7. X.-X. Du, B. Tian, Q.-X. Qu, Y.-Q. Yuan and X.-H. Zhao, Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma. Chaos Solitons Fract. 134 (2020) 109709. [CrossRef] [Google Scholar]
  8. P.G. Estëvez and J. Prada, Lump solutions for PDEs: algorithmic construction and classification. J. Nonlinear Math. Phys. 15 (2008) 166–75. [CrossRef] [Google Scholar]
  9. X.-Y. Gao, Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas. Appl. Math. Lett. 91 (2019) 165–172. [CrossRef] [Google Scholar]
  10. C. Garrett and J. Gemmrich, Rogue waves. Physics Today 62 (2009) 62–63. [CrossRef] [Google Scholar]
  11. X.-Y. Gao, Y.-J. Guo and W.-R. Shan, Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bácklund transformations. Appl. Math. Lett. 104 (2020) 106170. [CrossRef] [Google Scholar]
  12. R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys, Rev. Lett. 27 (1971) 1192–1194. [CrossRef] [Google Scholar]
  13. R. Hirota, Direct method in soliton theory, in Solitons, edited by R.K. Bullough, P.J. Caudrey. Springer, Berlin, (1980). [Google Scholar]
  14. C.-C. Hu, B. Tian, H.-M. Yin, C.-R. Zhang and Z. Zhang, Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)- dimensional generalized Kadomtsev-Petviashvili equation in a fluid. Comput. Math. Appl. 78 (2019) 166–177. [CrossRef] [Google Scholar]
  15. L. Huangand Y. Chen, Lump solutions and interaction phenomenon for (2 + 1)-dimensional Sawada-Kotera equation. Theor. Phys. 67 (2017) 473–478. [Google Scholar]
  16. K. Imai, Dromion and lump solutions of the Ishimori-I equation. Progr. Theor. Phys. 98 (1997) 1013–1023. [CrossRef] [Google Scholar]
  17. B.-Q. Li and Y.-L. Ma, Multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid. Comput. Math. Appl. 76 (2018) 204–214. [CrossRef] [Google Scholar]
  18. B.-Q. Li and Y.-L. Ma, Solitons resonant behavior for a waveguide directional coupler system in optical fbers. Opt. Quantum Electron. 50 (2018) 270. [CrossRef] [Google Scholar]
  19. B.-Q. Li, Y.-L. Ma, L.-P. Mo and Y.-Y. Fu, The N-loop soliton solutions for (2 + 1)-dimensional Vakhnenko equation. Comput. Math. Appl. 74 (2017) 504–512. [CrossRef] [Google Scholar]
  20. Z. Lu and Y. Chen, Construction of rogue wave and lump solutions for nonlinear evolution equations. Eur. Phys. J. B 88 (2015) 1–5. [EDP Sciences] [Google Scholar]
  21. Z. Lu, E.M. Tian and R. Grimshaw, Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation. Wave Motion 40 (2004) 123–35. [CrossRef] [Google Scholar]
  22. Y.-L. Ma, Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers. Nonlinear Dyn. 97 (2019) 95–105. [CrossRef] [Google Scholar]
  23. Y.-L. Ma and B.-Q. Li, Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: Hidden rogue wave and hidden soliton. Comput. Math. Appl. 78 (2019) 827–839. [CrossRef] [Google Scholar]
  24. Y.-L. Ma and B.-Q. Li, Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation. AIMS Math. 5 (2020) 1162–1176. [CrossRef] [Google Scholar]
  25. Y.-L. Ma and B.-Q., Rogue wave solutions, soliton and rogue wave mixed solution for a generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation in fluids. Mod. Phys. Lett. B 32 (2018) 1850358. [Google Scholar]
  26. S.V. Manakov and V.E. Zakharov, Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction. Phys. Lett. A 63 (1977) 205–6. [CrossRef] [Google Scholar]
  27. S. Manukure, Y. Zhou and W.X. Ma, Lump solutions to a (2 + 1)-dimensional extended KP equation. Comput. Math. Appl. 75 (2018) 2414–2419. [CrossRef] [Google Scholar]
  28. H.E. Nistazakis, D.J. Frantzeskakis and B.A. Malomed, Collisions between spatiotemporal solitons of different dimensionality in a planar waveguide. Phys. Rev. E 64 (2001) 026604. [Google Scholar]
  29. H.-L. Si and B.-Q. Li, Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials. Optik 166 (2018) 49–55. [Google Scholar]
  30. H.-Q. Sun and A.-H. Chen, Interactional solutions of a lump and a solitary wave for two higher-dimensional equations. Nonlinear Dyn. 94 (2018) 1753–1762. [Google Scholar]
  31. Y. Tang, S. Tao and Q. Guan, Lumpsolitons and the interaction phenomena of them for two classes of nonlinear evolution equations. Comput. Math. Appl. 72 (2016) 2334–2342. [Google Scholar]
  32. X. Wang, Y.Q. Li, F. Huang and Y. Chen, Rogue wave solitons of AB system. Commun. Nonlinear Sci. Numer. Simul. 20 (2015) 434–442. [Google Scholar]
  33. C. Wang, Z. Dai and C. Liu, Interaction between kink solitary wave and rogue wave for (2 + 1)-dimensional Burgers equation. Mediterr. J. Math. 13 (2016) 1087–1098. [Google Scholar]
  34. M. Wang, B. Tian, Y. Sun and Z. Zhang, Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear. Comput. Math. Appl. 79 (2020) 576–587. [Google Scholar]
  35. A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theorem. Springer and HEP, Berlin (2009) [Google Scholar]
  36. A.-M. Wazwaz and S.A. El-Tantawy, New (3+1)-dimensional equations of Burgers type and Sharma-Tasso-Olver type: multiple-soliton solutions. Nonlinear Dyn. 87 (2017) 2457–2461. [Google Scholar]
  37. H.W. Yang, X. Chen, M. Guo and Y.D. Chen, A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Nonlinear Dyn. 91 (2018) 2019–2032. [Google Scholar]
  38. H.-M. Yin, B. Tian and X.-C. Zhao, Chaotic breathers and breather fission/fusion for a vector nonlinear Schrödinger equation in a birefringent optical fiber or wavelength division multiplexed system. Appl. Math. Comput. 368 (2020) 124768. [Google Scholar]
  39. C.-R. Zhang, B. Tian, Q.-X. Qu, L. Liu and H.-Y. Tian, Vector bright solitons and their interactions of the couple Fokas-Lenells system in a birefringent optical fiber. Z. Angew. Math. Phys. 71 (2020) 18. [Google Scholar]

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