Open Access
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 2
Number of page(s) 10
Published online 03 February 2022
  1. C.L. Chen and S.Y. Lou, CTE solvability and exact solution to the Broer-Kaup system. Chin. Phys. Lett. 30 (2013) 110202. [CrossRef] [Google Scholar]
  2. X.P. Cheng, S.Y. Lou, C.L. Chen and X.Y. Tang, Interactions between solitons and other nonlinear Schrödinger waves. Phys. Rev. E 89 (2014) 1–14. [Google Scholar]
  3. W.G. Cheng, B. Li and Y. Chen, Nonlocal symmetry and exact solutions of the (2+1)-dimensional breaking soliton equation. Commun. Nonlinear Sci. Numer. Simulat. 29 (2015) 198–207. [CrossRef] [Google Scholar]
  4. C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura, Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967) 1095–1097. [CrossRef] [Google Scholar]
  5. G.A. Guthrie, More non-local symmetries of the KdV equation. J. Phys. A: Math. Gen. 26 (1993) L905–L908. [CrossRef] [Google Scholar]
  6. R. Hirota, The Direct Method in Soliton Theory. Cambridge University Press, Cambridge (2004). [CrossRef] [Google Scholar]
  7. X.R. Hu and Y. Chen, Nonlocal symmetries, consistent Riccati expansion integrability, and their applications of the (2+1)-dimensional Broer-Kaup-Kupershmidt system. Chin. Phys. B 24 (2015) 090203. [CrossRef] [Google Scholar]
  8. H.C. Hu, X. Hu and B.F. Feng, Nonlocal symmetry and consistent tanh expansion method for the coupled integrable dispersionless equation. Z. Naturforsch. A 71 (2016) 235–240. [CrossRef] [Google Scholar]
  9. X.R. Hu, S.Y. Lou and Y. Chen, Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation. Phys. Rev. E 85 (2012) 056607. [CrossRef] [PubMed] [Google Scholar]
  10. Y.Y. Li and H.C. Hu, Nonlocal symmetries and interaction solutions of the Benjamin-Ono equation. Appl. Math. Lett. 75 (2018) 18–23. [CrossRef] [MathSciNet] [Google Scholar]
  11. S.Y. Lou, Residual symmetries and Bäcklund transformations. Preprint arXiv:1308.1140v1 [nlin.SI] (2013). [Google Scholar]
  12. S.Y. Lou, Consistent Riccati expansion for integrable systems. Stud. Appl. Math. 134 (2015) 372–402. [CrossRef] [MathSciNet] [Google Scholar]
  13. S.Y. Lou, X.R. Hu and Y. Chen, Nonlocal symmetries related to Bäcklund transformation and their applications. J. Phys. A: Math. Theor. 45 (2012) 155209. [CrossRef] [Google Scholar]
  14. V.B. Matveev, and M.A. Salle, Darboux Transformations and Solitons, Springer-Verlin, Berlin (1991). [CrossRef] [Google Scholar]
  15. P.J. Olver, J. Sanders and J.P. Wang, Ghost symmetries. J. Nonlinear Math. Phys. 20 (2002) 164–172. [Google Scholar]
  16. B. Ren, Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method. Phys. Scr. 90 (2015) 065206. [CrossRef] [Google Scholar]
  17. B. Ren, Symmetry reduction related with nonlocal symmetry for Gardner equation. Commun. Nonlinear Sci. Numer. Simulat. 42 (2017) 456–463. [CrossRef] [Google Scholar]
  18. B. Ren, W.X. Ma and J. Yu, Characteristics and interactions of solitary and lump waves of a (2 + 1)-dimensional coupled nonlinear partial differential equation. Nonlinear Dyn. 96 (2019) 717–727. [CrossRef] [Google Scholar]
  19. B. Ren, J. Lin and Z.M. Lou, Consistent Riccati expansion and rational solutions of the Drinfel’d-Sokolov-Wilson equation. Appl. Math. Lett. 105 (2020) 106326. [CrossRef] [MathSciNet] [Google Scholar]
  20. B. Ren, X.P. Cheng and J. Lin, The (2+1)-dimensional Konopelchenko-Dubrovsky equation: nonlocal symmetries and interaction solutions. Nonlinear Dyn. 86 (2016) 1855–1862. [CrossRef] [Google Scholar]
  21. C. Rogers and W.K. Schief, Bäcklund and Darboux Transformation, Geometry and Modern Applications in Soliton Theory, Cambridge University Press, Cambridge (2002). [Google Scholar]
  22. X.Y. Tang, S.Y. Lou and Y. Zhang, Localized excitations in (2+1)-dimensional systems. Phys. Rev. E 66 (2002) 046601. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y.H. Wang, CTE method to the interaction solutions of Boussinesq-Burgers equations. Appl. Math. Lett. 38 (2014) 100–105. [CrossRef] [MathSciNet] [Google Scholar]
  24. Y.H. Wang and H. Wang, Symmetry analysis and CTE solvability for the (2+1)-dimensional Boiti-Leon-Pempinelli equation. Phys. Scr. 89 (2014) 125203. [CrossRef] [Google Scholar]
  25. 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]
  26. J. Weiss, M. Tabor and G. Carnevale, The Painlevé property for partial differential equations. J. Math. Phys. 24 (1983) 522–526. [CrossRef] [MathSciNet] [Google Scholar]

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