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New types of interaction solutions to the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

Yuexing Bai

School of Information Engineering, Shanghai Maritime University, Shanghai 200135, China

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Temuerchaolu

College of Arts and Sciences, Shanghai Maritime University, Shanghai 200135, China

E-mail Address: tmchaolu@shmtu.edu.cn

Corresponding author.

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Yan Li

College of Arts and Sciences, Shanghai Maritime University, Shanghai 200135, China

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, and

Sudao Bilige

Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China

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https://doi.org/10.1142/S0217984920502371Cited by:2 (Source: Crossref)

Abstract

In this paper, with the aid of symbolic computation system Maple, and based on the simplified Hirota method and ansatz technique, we discussed the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation with $p = 3$ to obtain lump solutions, lump–kink solutions and three classes of interaction solutions. Comparing our new results with other researchers’ results shows that using this method gives the more opportunity to solve the nonlinear partial differential equations that appear in mathematics, physics, biological engineering and other fields. We also presented profiles of new lump solution, lump–kink solutions and interaction solutions as illustrative examples.

Keywords:

References

1. A. Bekir et al., Pramana 81(2) (2013) 203. Crossref, Web of Science, ADS, Google Scholar
2. M. A. Alejo, J. Nonlinear Math. Phys. 19(1) (2012) 119. Link, Web of Science, Google Scholar
3. Z. J. Xiao, B. Tian and Y. Sun, Mod. Phys. Lett. B 32(2) (2018) 1750170. Link, Web of Science, ADS, Google Scholar
4. H. Ali, On General Form of Tanh Method and Its Application to Medical Problems (Springer, Singapore, 2017). Crossref, Google Scholar
5. K. R. Raslan, K. K. Ali and M. A. Shallal, Chaos, Solitons and Fractals 103 (2017) 404. Crossref, Web of Science, ADS, Google Scholar
6. Y. Pandir and A. Yildirim, Waves Random Complex Media 7 (2017) 1. Google Scholar
7. B. Kaur and R. K. Gupta, Nonlinear Dynam. 96(2) (2019) 837. Crossref, Web of Science, Google Scholar
8. Y. Pandir and H. H. Duzgun, Commun. Theor. Phys. 67(1) (2017) 9. Crossref, Web of Science, ADS, Google Scholar
9. M. S. Islam, M. A. Akbar and K. Khan, Cogent Math. 4(1) (2017). Crossref, Web of Science, Google Scholar
10. S. Bilige and T. Chaolu, Appl. Math. Comput. 216 (2010) 3146. Web of Science, Google Scholar
11. W. X. Ma, T. W. Huang and Y. Zhang, Phys. Scripta 82 (2010) 065003. Crossref, Web of Science, Google Scholar
12. W. X. Ma and J.-H. Lee, Chaos Soliton. Fract. 42 (2009) 1356. Crossref, Web of Science, ADS, Google Scholar
13. R. Hirota, The Direct Method in Soliton Theory (Cambridge University Press, New York, 2004). Crossref, Google Scholar
14. Y. Matsuno, Bilinear Transformation Method (Academic Press, New York, 1984). Google Scholar
15. H. Ryogo, Phys. Rev. L 27 (1971) 1192. Crossref, Web of Science, Google Scholar
16. W. X. Ma and Y. Zhou, J. Diff. Equ. 264 (2018) 30577. Crossref, Web of Science, Google Scholar
17. L. Zou et al., Mod. Phys. Lett. B (2018) 1850104. Link, Web of Science, Google Scholar
18. J. Y. Yang, W. X. Ma and Z. Qin, Anal. Math. Phys. 8 (2018) 427. Crossref, Web of Science, Google Scholar
19. W. X. Ma, X. Yong and H.-Q. Zhang, Comput. Math. Appl. 75(1) (2018) 289. Crossref, Web of Science, Google Scholar
20. A. Nakamura, Phys. Lett. A 88(2) (1982) 55. Crossref, Web of Science, ADS, Google Scholar
21. J. Q. Lü and S. Bilige, Anal. Math. Phys. 9 (2019) 1497. Crossref, Web of Science, Google Scholar
22. W. X. Ma and E. G. Fan, Comput. Math. Appl. 61 (2011) 950. Crossref, Web of Science, Google Scholar
23. W. X. Ma and A. Abdeljabbar, Appl. Math. Lett. 25(10) (2012) 1500. Crossref, Web of Science, Google Scholar
24. W. X. Ma, Z. Qin and X. Lü, Nonlinear Dynam. 84 (2016) 923. Crossref, Web of Science, Google Scholar
25. J. Lü, S. Bilige and X. Q. Gao, Int. J. Nonlinear Sci. Numer. Simul. 20(1) (2018) 34. Google Scholar
26. A. M. Wazwaz, Commun. Nonlinear Sci. Numer. Simul. 17(2) (2012) 491. Crossref, Web of Science, ADS, Google Scholar
27. W. X. Ma, Studies Nonlinear Sci. 2(4) (2011) 140. Google Scholar
28. C. Gilson et al., Proc. Roy. Soc. A-Math. Phys. Eng. Sci. 452 (1996) 223. Crossref, ADS, Google Scholar
29. W. X. Ma, J. Phys. Conf. Ser. 411 (2013) 012021. Crossref, ADS, Google Scholar