Research PaperNo Access

Painlevé analysis, dark and singular structures for pseudo-parabolic type equations

Saima Arshed

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

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Nauman Raza

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

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, and

Melike Kaplan

https://orcid.org/0000-0001-5700-9127

Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu, Turkey

E-mail Address: mkaplan@kastamonu.edu.tr

Corresponding author.

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https://doi.org/10.1142/S0217984922501044Cited by:5 (Source: Crossref)

Abstract

In this paper, two important pseudo-parabolic type equations are studied for extracting soliton solutions via the generalized projective riccati equations method. These equations are Oskolkov equation and Oskolkov–Benjamin–Bona–Mahony–Burgers equation. The proposed method extracts dark soliton and singular soliton. Furthermore, the Painlevé test (P-test) has also been employed on pseudo-parabolic type equations for investigating integrability. The proposed equations are proved to be integrable by P-test. The numerical simulations have also been carried out by 3D and 2D graphs of some of the obtained solutions.

Keywords:

References

1. N. A. Kudryashov, Analytical Theory of Nonlinear Differential Equation (Institute of Computer Investigations, Moscow, 2004). Google Scholar
2. P. G. Drazin, Nonlinear Systems (Cambridge University Press, 1992). Crossref, Google Scholar
3. I. Herron, C. McCalla and R. Mickens, Appl. Math. Lett. 107 (2020) 106496. Crossref, Web of Science, Google Scholar
4. S. W. McCue, M. El-Hachem and M. J. Simpson, Appl. Math. Lett. 114 (2021) 106918. Crossref, Web of Science, Google Scholar
5. V. S. Erturk and P. Kumar, Chaos Solitons Fractals 139 (2020) 110280. Crossref, Web of Science, Google Scholar
6. N. A. Kudryashov, Optik 219 (2020) 165193. Crossref, Web of Science, ADS, Google Scholar
7. S. D. Eidelman, S. D. Ivasyshen and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-differential Equations of Parabolic Type (Birkhäuser, 2004). Crossref, Google Scholar
8. L. W. Whitet, Appl. Anal. 12 (2007) 251. Crossref, Web of Science, Google Scholar
9. P. Luo, Math. Methods Appl. Sci. 38 (2014) 2636. Crossref, Web of Science, Google Scholar
10. H. Rezazadeh, M. Inc and D. Baleanu, Front. Phys. 8 (2020) 332. Crossref, Web of Science, Google Scholar
11. N. Raza and S. Arshed, Ain Shams Eng. J. 11 (2020) 1237. Crossref, Web of Science, Google Scholar
12. A. R. Seadawy, M. Bilal, M. Younis, S. T. R. Rizvi, S. Althobaiti and M. M. Makhlouf, Chaos Solitons Fractals 144 (2021) 110669. Crossref, Web of Science, Google Scholar
13. M. Kaplan and M. N. Ozer, Opt. Quantum Electron. 50 (2018) 33. Crossref, Web of Science, Google Scholar
14. N. Raza, U. Afzal, A. R. Butt and H. Rezazadeh, Opt. Quantum Electron. 51 (2019) 107, https://doi.org/10.1007/s11082-019-1813-0. Crossref, Web of Science, Google Scholar
15. K. Hosseini, D. Kumar, M. Kaplan and E. Y. Bejarbaneh, Commun. Theor. Phys. 68 (2017) 761. Crossref, Web of Science, ADS, Google Scholar
16. N. Raza, M. Abdullah, A. R. Butt, I. G. Murtaza and S. Sial, Opt. Quantum Electron. 50 (2018) 177, https://doi.org/10.1007/s11082-018-1444-x. Crossref, Web of Science, Google Scholar
17. N. Raza, R. Rahman, A. Seadawy and A. Jhangeer, Int. J. Mod. Phys. B (2021), https://doi.org/10.1142/S0217979221501575. Google Scholar
18. C. Gu, Soliton Theory and its Applications (Springer-Verlag, Berlin, 1995). Crossref, Google Scholar
19. O. F. Gozukizil and S. Akcagil, Adv. Differ. Equ. 2013 (2013) 1. Crossref, Web of Science, Google Scholar
20. S. Akcagi, T. Aydemir and O. F. Gozukizil, New Trends Math. Sci. 4 (2016) 51. Crossref, Google Scholar
21. K. Hosseini, E. Y. Bejarbaneh, A. Bekir and M. Kaplan, Opt. Quantum Electron. 49 (2017) 1. Crossref, Web of Science, Google Scholar
22. R. S. Saha, Mod. Phys. Lett. B 34 (2020) 2050012. Link, Web of Science, Google Scholar
23. O. A. llhan, H. Bulut, T. A. Sulaiman and H. M. Baskonus, Indian J. Phys. 92 (2018) 999. Crossref, Web of Science, ADS, Google Scholar
24. A. I. Aristov, Comput. Math. Math. Phys. 58 (2018) 1792. Crossref, Web of Science, Google Scholar
25. R. Conte and M. Musette, J. Phys. A: Math. Gen. 25 (1992) 56095623. Crossref, Google Scholar
26. Z. Y. Yan, Chaos Solitons Fractals 16 (2003) 759766. Google Scholar
27. M. J. Ablowitz, A. Ramani and H. Segur, J. Math. Phys. 21 (1980) 1006. Crossref, Web of Science, ADS, Google Scholar
28. J. Weiss, M. Tabor and G. Carnevale, J. Math. Phys. 24 (1983) 522. Crossref, Web of Science, ADS, Google Scholar
29. A. Bekir, Chaos Solitons Fractals 32 (2007) 449. Crossref, Web of Science, ADS, Google Scholar