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New graphical observations for KdV equation and KdV–Burgers equation using modified auxiliary equation method

Ghazala Akram

https://orcid.org/0000-0003-0288-9299

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

E-mail Address: toghazala2003@yahoo.com

Corresponding author.

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Maasoomah Sadaf

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

E-mail Address: maasoomahsadaf@yahoo.com

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, and

Iqra Zainab

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

E-mail Address: iqrazainab40@gmail.com

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https://doi.org/10.1142/S0217984921505205Cited by:9 (Source: Crossref)

Abstract

This study is made to extract the exact solutions of Korteweg–de Vries–Burgers (KdVB) equation and Korteweg–de Vries (KdV) equation. The original idea of this work is to investigate KdV equation and KdVB equation for possible closed form solutions by employing the modified auxiliary equation (MAE) method. Exact traveling wave solutions of the considered equations are retrieved in the form of trigonometric and hyperbolic functions. Kink, periodic and singular wave patterns are obtained from the constructed solutions. The graphical illustration of the wave solutions is presented using 3D-surface plots to acquire the understanding of physical behavior of the obtained results up to possible extent.

Keywords:

References

1. N. Sajid and G. Akram, Mod. Phys. Lett. B 35(5) (2021) 2150086. Link, Web of Science, ADS, Google Scholar
2. M. M. Miah, A. R. Seadawy, H. M. S. Ali and M. A. Akbar, J. Ocean Eng. Sci. 5(3) (2020) 269. Crossref, Web of Science, Google Scholar
3. C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Phys. Rev. Lett. 19(19) (1967) 1095. Crossref, Web of Science, ADS, Google Scholar
4. P. C. Jain, R. Shankar and D. Bhardwaj, Chaos Solitons Fractals 8(6) (1997) 943. Crossref, Web of Science, ADS, Google Scholar
5. N. Faraz, M. Sadaf, G. Akram, I. Zainab and Y. Khan, Results Phys. 25 (2021) 104217. Crossref, Web of Science, Google Scholar
6. L. R. T. Gardner, G. A. Gardner and A. H. A. Ali, Comput. Methods Appl. Mech. Eng. 92 (1991) 231. Crossref, Web of Science, ADS, Google Scholar
7. L. R. T. Gardner and A. H. A. Ali, Proc. Int. Conf. Modeling and Simulation, Vol. 1 (1988), p. 81. Google Scholar
8. G. Akram, M. Sadaf, S. Arshed and F. Sameen, Optik: Int. J. Light Electron Opt. 241 (2021) 167051. Crossref, Google Scholar
9. A. A. Soliman, A. H. A. Ali and K. R. Raslan, Appl. Math. Model. 33(2) (2009) 1107. Crossref, Web of Science, Google Scholar
10. V. D. David, M. Nazari, V. Barat, F. Salah and Z. Abdul Aziz, J. Appl. Math. 2013 (2013) 795818. Crossref, Web of Science, Google Scholar
11. Z. Feng and Y. Huang, Commun. Pure Appl. Anal. 6(2) (2007) 429. Crossref, Web of Science, Google Scholar
12. H. Rezazadeh, H. Tariq, M. Eslami, M. Mirzazadeh and Q. Zhou, Chin. J. Phys. 56 (2018) 2805. Crossref, Web of Science, ADS, Google Scholar
13. J. Sabi’u, H. Rezazadeh, H. Tariq and A. Bekir, Mod. Phys. Lett. B 33 (2019) 1950308. Link, Web of Science, ADS, Google Scholar
14. D. Kumar and S. Kumar, Eur. Phys. J. Plus 135162 (2020). Google Scholar
15. C. H. C. Hussin, A. I. M. Ismail, A. Kilicman and A. Azmi, Math. Stat. 8 (2020) 9. Crossref, Google Scholar
16. Y. Xie, S. Tang and D. Feng, Pramana: J. Phys. 78(4) (2012) 499. Crossref, Web of Science, ADS, Google Scholar
17. H. Triki, T. Ak and A. Biswas, Appl. Comput. Math. 16(2) (2017) 168. Web of Science, Google Scholar
18. E. Alimirzaluo and M. Nadjafikhah, J. Phys. Commun. 3 (2019) 035025. Crossref, Web of Science, Google Scholar
19. V. S. Kumar, H. Razazadeh, M. Eslami, F. Izadi and M. S. Osman, Int. J. Appl. Comput. Math. 127 (2019) 5. Google Scholar
20. N. Liu, Appl. Math. Lett. 104 (2020) 106256. Crossref, Web of Science, Google Scholar
21. M. M. A. Khater, R. A. M. Attia and D. Lu, Math. Comput. Appl. 24(1) (2019) 1. Google Scholar
22. M. S. Osman, D. Lu, M. M. A. Khater and R. A. M. Attia, Optik: Int. J. Light Electron Opt. 192 (2019) 1. Crossref, Google Scholar
23. G. Akram and I. Zainab, Optik: Int. J. Light Electron Opt. 208 (2020) 164420. Crossref, Google Scholar
24. M. M. A. Khater, R. A. M. Attia and D. Lu, AIP Adv. 9(2) (2019) 1. Crossref, Web of Science, Google Scholar
25. A. R. Seadawy, D. Lu and M. Iqbal, Pramana: J. Phys. 93 (2019) 10. Crossref, Web of Science, ADS, Google Scholar
26. A. Asghar, A. R. Seadawy and D. Lu, Adv. Differ. Equ. 232 (2018) 2018. Google Scholar
27. M. Arshad, A. R. Seadawy and D. Lu, J. Electromagn. Waves Appl. 31(16) (2017) 1711. Crossref, Web of Science, Google Scholar
28. I. Ahmed, A. R. Seadawy and D. Lu, Phys. Scr. 94(5) (2019) 055205. Crossref, Web of Science, Google Scholar
29. A. R. Seadawy, D. Kumar, K. Hosseini and F. Samadani, Results Phys. 9 (2018) 1631. Crossref, Web of Science, ADS, Google Scholar
30. N. Cheemaa, A. R. Seadawy and S. Chen, Eur. Phys. J. Plus 133(12) (2018) 547. Crossref, Web of Science, Google Scholar
31. N. Cheemaa, A. R. Seadawy and S. Chen, Eur. Phys. J. Plus 134(3) (2019) 117. Crossref, Web of Science, Google Scholar
32. Y. S. Özkan, E. Yaşar and A. R. Seadawy, Phys. Scr. 95(8) (2020) 085205. Crossref, Web of Science, Google Scholar
33. A. R. Seadawy and N. Cheemaa, Indian J. Phys. 94(1) (2020) 117. Crossref, Web of Science, ADS, Google Scholar
34. I. Ali, A. R. Seadawy, S. T. Rizvi, M. Younis and K. Ali, Int. J. Mod. Phys. B 34(30) (2020) 2050283. Link, Web of Science, ADS, Google Scholar
35. S. T. Rizvi, A. R. Seadawy, F. Ashraf, M. Younis, H. Iqbal and D. Baleanu, Results Phys. 19 (2020) 103661. Crossref, Web of Science, Google Scholar
36. U. Younas, A. R. Seadawy, M. Younis and S. T. Rizvi, Int. J. Mod. Phys. B 34(30) (2020) 2050291. Link, Web of Science, ADS, Google Scholar
37. M. M. Khader, K. M. Saad, Z. Hammouch and D. Baleanu, Appl. Numer. Math. 161 (2021) 137. Crossref, Web of Science, Google Scholar
38. N. Cheemaa, A. R. Seadawy, T. G. Sugati and D. Baleanu, Results Phys. 19 (2020) 103480. Crossref, Web of Science, Google Scholar
39. C. Park, R. I. Nuruddeen, K. K. Ali, L. Muhammad, M. S. Osman and D. Baleanu, Adv. Differ. Equ. 2020(1) (2020) 627. Crossref, Web of Science, Google Scholar
40. S. A. El-Tantawy, S. A. Shan, N. Mustafa, M. H. Alshehri, F. Z. Duraihem and N. B. Turki, Eur. Phys. J. Plus 136 (2021) 561. Crossref, Web of Science, Google Scholar
41. N. H. Aljahdaly and S. A. El-Tantawy, Mathematics 9(4) (2021) 432. Crossref, Web of Science, Google Scholar
42. B. S. Kashkari and S. A. El-Tantawy, Eur. Phys. J. Plus 136 (2021) 121. Crossref, Web of Science, Google Scholar
43. S. A. El-Tantawy, Chaos Solitons Fractals 93 (2016) 162. Crossref, Web of Science, ADS, Google Scholar
44. S. A. El-Tantawy, Astrophys. Space Sci. 361 (2016) 249. Crossref, Web of Science, ADS, Google Scholar
45. S. T. Rizvi, A. R. Seadawy, I. Ali, I. Bibi and M. Younis, Mod. Phys. Lett. B 34(35) (2020) 2050399. Link, Web of Science, ADS, Google Scholar
46. A. R. Seadawy and N. Cheemaa, Physica A 529 (2019) 121330. Crossref, Web of Science, Google Scholar
47. A. R. Seadawy and N. Cheemaa, Mod. Phys. Lett. B 33(18) (2019) 1950203. Link, Web of Science, ADS, Google Scholar