Research PapersNo Access

Symbolic computations: Dispersive soliton solutions for (3+1)-dimensional Boussinesq and Kadomtsev–Petviashvili dynamical equations and its applications

Aly R. Seadawy

http://orcid.org/0000-0002-7412-4773

Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

E-mail Address: Aly742001@yahoo.com

Corresponding author.

Search for more papers by this author

Kalim U. Tariq

Department of Mathematics, Mirpur University of Science and Technology, Mirpur (AJK) 10250, Pakistan

Search for more papers by this author

, and

Jian-Guo Liu

College of Computer, Jiangxi University of Traditional Chinese Medicine, Jiangxi 330004, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0217979219503429Cited by:5 (Source: Crossref)

Abstract

In this paper, the auxiliary expansion equation method is applied to compute the analytical wave solutions for (3+1)-dimensional Boussinesq and Kadomtsev–Petviashvili (KP) equations. A simple transformation is carried out to reduce the set of nonlinear partial differential equations (NPDEs) into ODEs. These obtained results hold numerous traveling wave solutions that are of key importance in elucidating some physical circumstance.

Keywords:

PACS: 02.30.Jr, 05.45.Yv, 47.10.A, 47.35.+i, 47.35.Fg

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. H. Gard and P. N. Hu, Phys. Fluids 10, 2596 (1967). Web of Science, ADS, Google Scholar
2. N. J. Zabusky, A synergetic approach to problems of nonlinear dispersive wave propagation and interaction, in Nonlinear Partial Differential Equations, ed. W. F. Ames (Academic Press, New York, 1967). Google Scholar
3. A. Seadawy and J. Manafian, Results Phys. 8, 1158 (2018). Web of Science, ADS, Google Scholar
4. B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl. 15, 539 (1970). ADS, Google Scholar
5. A. R. Seadawy and S. Z. Alamri, Results Phys. 8, 286 (2018). Web of Science, ADS, Google Scholar
6. A. R. Seadawy, Pramana J. Phys. 89, 1 (2017). Web of Science, ADS, Google Scholar
7. R. Hirota and M. Ito, J. Phys. Soc. Jpn. 52, 774 (1983). ADS, Google Scholar
8. A. Seadawy, Eur. Phys. J. Plus 132, 518 (2017). Web of Science, Google Scholar
9. A. H. Khater, D. K Callebaut and A. R. Seadawy, Phys. Scripta 74, 384 (2006). Web of Science, ADS, Google Scholar
10. R. S. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves (Cambridge University Press, Cambridge, 1997). Google Scholar
11. V. Varlamov, Nonlinear Anal. Theory Methods Appl. 46, 699 (2001). Web of Science, Google Scholar
12. C. Gardner et al., Phys. Rev. Lett. 19, 1095. Web of Science, Google Scholar
13. R. Hirota, Phys. Rev. Lett. 27, 1192 (1971). Web of Science, ADS, Google Scholar
14. M. Ito, J. Phys. Soc. Jpn. 49, 771 (1980). Web of Science, ADS, Google Scholar
15. M. J. Ablowitz and P. A. Clarkson, Soliton, Nonlinear Evolution Equations and Inverse Scattering (Cambridge University Press, USA, 1991). Google Scholar
16. E. S. Selima, A. R. Seadawy and X. Yao, Eur. Phys. J. Plus 131 (2016). Google Scholar
17. M. L. Wang, Phys. Lett. A 199, 169 (1995). Web of Science, ADS, Google Scholar
18. S. K. Liu et al., Phys. Lett. A 289, 69 (2001). Web of Science, ADS, Google Scholar
19. Y. Chen, Z. Yan and H. Zhan, Phys. Lett. A 307, 107 (2003). Web of Science, ADS, Google Scholar
20. Y. B. Zhou, M. L. Wang and Y. M. Wang, Phys. Lett. A 308, 31 (2003). Web of Science, ADS, Google Scholar
21. Y. Liang, J. Interdiscip. Math. 17, 565 (2014). Google Scholar
22. J. H. He, Chaos Soliton. Fract. 19, 847 (2004). Web of Science, ADS, Google Scholar
23. A. Seadawy, M. Arshad and D. Lu, Eur. Phys. J. Plus 132, 1 (2017). Web of Science, Google Scholar
24. K. U.-H. Tariq and A. Seadawy, Results Phys. 7, 1143 (2017). Web of Science, ADS, Google Scholar
25. M. Arshad et al., Chin. J. Phys. 55, 780 (2017). Web of Science, ADS, Google Scholar
26. X. Li and M. Wang, Phys. Lett. A 361, 115 (2007). Web of Science, ADS, Google Scholar
27. M. A. Helal and A. R. Seadawy, Comput. Math. Appl. 64, 3557 (2012). Web of Science, Google Scholar
28. A. R. Seadawy, Eur. Phys. J. Plus 132, 1 (2017). Web of Science, Google Scholar
29. S. Y. Lai, Y. H. Wu and Y. Zhou, Comput. Math. Appl. 56, 339 (2008). Web of Science, Google Scholar
30. M. A. Helal, A. R Seadawy and M. H. Zekry, Chin. J. Phys. 55, 378 (2017). Web of Science, Google Scholar
31. R. Abazari, Comput. Fluids 39, 1957 (2010). Web of Science, Google Scholar
32. S. Kutluay, A. Esen and O. Tasbozan, Appl. Math. Comput. 217, 384 (2010). Web of Science, Google Scholar
33. D. Lu et al., Results Phys. 7, 899 (2017). Web of Science, ADS, Google Scholar
34. A. H. Khater et al., Eur. Phys. J. D 39, 237 (2006). Web of Science, ADS, Google Scholar
35. A. R. Seadawy, L. Dianchen and Y. Chen, J. Taibah Univ. Sci. 11, 623 (2017). Web of Science, Google Scholar
36. A. R. Seadawy, Phys. A Stat. Mech. Appl. Phys. A 455, 44 (2016). Web of Science, ADS, Google Scholar
37. A. R. Seadawy, Int. J. Comput. Methods 15, 1850017 (2018). Link, Web of Science, Google Scholar
38. A. R. Seadawy, Appl. Math. Sci. 6, 4081 (2012). Google Scholar
39. X.-L. Gai et al., Int. J. Modern Phys. B 26, 1250062 (2012). Link, Web of Science, ADS, Google Scholar
40. J. Grey and M. M. Tom, oai:arXiv.org:1410.3158 (2014). Google Scholar
41. S. C. Mohapatra and C. Guedes Soarein, in Comparing solutions of the coupled Boussinesq equations in shallow water, (eds.) Maritime Technology and Engineering Guedes Soares & Santos (Taylor & Francis Group, London, 2015), ISBN 978-1-138-02727-5. Google Scholar