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All issues Volume 15 (2020) Math. Model. Nat. Phenom., 15 (2020) 61 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Article Number 61
Number of page(s) 12
DOI https://doi.org/10.1051/mmnp/2020018
Published online 03 December 2020
  1. A.R. Adem, M. Mirzazadeh, Q. Zhou and K. Hosseini, Multiple soliton solutions of the Sawada–Kotera equation with a nonvanishing boundary condition and the perturbed Korteweg de Vries equation by using the multiple exp-function scheme. Adv. Math. Phys. 2019 (2019) 3175213. [Google Scholar]
  2. X.X. Du, B. Tian and Y. Yin, Lump, mixed lump-kink, breather and rogue waves for a B-type Kadomtsev–Petviashvili equation. Waves Random Complex Media (2019), doi. 10.1080/17455030.2019.1566681. [Google Scholar]
  3. L.L. Feng and T.T. Zhang, Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation. Appl. Math. Lett. 78 (2018) 133–140. [CrossRef] [Google Scholar]
  4. C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura, Method for solving the Korteweg-deVries equation. Phys. Rev. Lett. 19 (1967) 1095–1097. [CrossRef] [Google Scholar]
  5. J. He and Y. Li, Designable integrability of the variable coefficient nonlinear Schrödinger equations. Studies Appl. Math. 126 (2011) 1–15. [CrossRef] [Google Scholar]
  6. J. He, L. Wang, L. Li, K. Porsezian and R. Erdlyi, Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation. Phys. Rev. E 89 (2014) 062917. [CrossRef] [Google Scholar]
  7. J.S. He, E.G. Charalampidis, P.G. Kevrekidis and D.J. Frantzeskakis, Rogue waves in nonlinear Schrödinger models with variable coefficients: Application to Bose–Einstein condensates. Phys. Lett. A 378 (2014) 577–583. [CrossRef] [Google Scholar]
  8. J. He, S. Xu and Y. Cheng, The rational solutions of the mixed nonlinear Schrödinger equation. AIP Adv. 5 (2015) 017105. [Google Scholar]
  9. W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simul. 43 (1997) 13–27. [CrossRef] [Google Scholar]
  10. W. Hereman and W. Zhuang, Symbolic software for soliton theory. Acta Appl. Math. 39 (1995) 361–378. [CrossRef] [MathSciNet] [Google Scholar]
  11. R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge (2004). [CrossRef] [Google Scholar]
  12. K. Hosseini, M. Aligoli, M. Mirzazadeh, M. Eslami and J.F. Gómez-Aguilar, Dynamics of rational solutions in a new generalized Kadomtsev–Petviashvili equation. Mod. Phys. Lett. B 33 (2019) 1950437. [CrossRef] [Google Scholar]
  13. 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]
  14. Y.F. Hua, B.L. Guo, W.X. Ma and X. Lü, Interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation for nonlinear waves. Appl. Math. Model. 74 (2019) 184–198. [CrossRef] [Google Scholar]
  15. M. Inc, K. Hosseini, M. Samavat, M. Mirzazadeh, M. Eslami, M. Moradi and D. Baleanu, N-wave and other solutions to the B-type Kadomtsev–Petviashvili equation. Ther. Sci. 23 (2019) 2027–2035. [CrossRef] [Google Scholar]
  16. J.G. Liu, and Y. He, Abundant lump and lump-kink solutions for the new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation. Nonlinear Dyn. 92 (2018) 1103–1108. [CrossRef] [Google Scholar]
  17. J.G. Liu and Q. Ye, Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics. Nonlinear Dyn. 96 (2019) 23–29. [CrossRef] [Google Scholar]
  18. J.G. Liu, J.Q. Du, Z.F. Zeng and B. Nie, New three-wave solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 88 (2017) 655–661. [CrossRef] [Google Scholar]
  19. J.G. Liu, M. Eslami, H. Rezazadeh and M. Mirzazadeh, Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation. Nonlinear Dyn. 95 (2019) 1027–1033. [CrossRef] [Google Scholar]
  20. X. Lü and W.X. Ma, Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation. Nonlinear Dyn. 85 (2016) 1217–1222. [CrossRef] [Google Scholar]
  21. W.X. Ma and Z. Zhu, Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm. Appl. Math. Comput. 218 (2012) 11871–11879. [Google Scholar]
  22. W.X. Ma, T. Huang and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82 (2010) 065003. [CrossRef] [Google Scholar]
  23. M.S. Osman and A.M. Wazwaz, A general bilinear form to generate different wave structures of solitons for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Math. Methods Appl. Sci. 42 (2019) 6277–6283. [CrossRef] [Google Scholar]
  24. M.S. Osman, M. Inc, J.G. Liu, K. Hosseini and A. Yusuf, Different wave structures and stability analysis for the generalized (2+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation. Phys. Scr. 95 (2020) 035229. [CrossRef] [Google Scholar]
  25. R. Pouyanmehr, K. Hosseini, R. Ansari and S.H. Alavi, Different wave structures to the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation. Int. J. Appl. Comput. Math. 5 (2019) 149. [CrossRef] [Google Scholar]
  26. W. Tan, H. Dai, Z. Dai and W. Zhong, Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation. Pramana J. Phys. 89 (2017) 77. [CrossRef] [Google Scholar]
  27. A.M. Wazwaz, Multiple-soliton solutions for the generalized (1+1)-dimensional and the generalized (2+1)-dimensional Ito equations. Appl. Math. Comput. 202 (2008) 840–849. [Google Scholar]
  28. A.M. Wazwaz, Multiple-soliton solutions for extended shallow water wave equations. Studies Math. Sci. 1 (2010) 21–29. [Google Scholar]
  29. A.M. Wazwaz, Two wave mode higher-order modified KdV equations: Essential conditions for multiple soliton solutions to exist. Int. J. Num. Methods Heat Fluid Flow 27 (2017) 2223–2230. [CrossRef] [Google Scholar]
  30. A.M. Wazwaz, Multiple complex and multiple real soliton solutions for the integrable sine-Gordon equation. Optik 172 (2018) 622–627. [CrossRef] [Google Scholar]
  31. A.M. Wazwaz, Multiple complex soliton solutions for the integrable KdV, fifth-order Lax, modified KdV, Burgers, and Sharma–Tasso–Olver equations. Chin. J. Phys. 59 (2019) 372–378. [CrossRef] [Google Scholar]
  32. A.M. Wazwaz, Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations. Appl. Math. Lett. 88 (2019) 1–7. [CrossRef] [Google Scholar]
  33. A.M. Wazwaz and L. Kaur, New integrable Boussinesq equations of distinct dimensions with diverse variety of soliton solutions. Nonlinear Dyn. 97 (2019) 83–94. [CrossRef] [Google Scholar]
  34. R. Zhang, S. Bilige, T. Fang and T. Chaolu, New periodic wave, cross-kink wave and the interaction phenomenon for the Jimbo–Miwa-like equation. Comput. Math. Appl. 78 (2019) 754–764. [CrossRef] [Google Scholar]
  35. Y. Zhou and W.X. Ma, Complexiton solutions to soliton equations by the Hirota method. J. Math. Phys. 58 (2017) 101511. [CrossRef] [Google Scholar]

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