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Symmetry reductions, explicit solutions, convergence analysis and conservation laws via multipliers approach to the Chen–Lee–Liu model in nonlinear optics

Aliyu Isa Aliyu

Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa 7156, Nigeria

E-mail Address: aliyu.isa@fud.edu.ng

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Mustafa Inc

http://orcid.org/0000-0003-4996-8373

Department of Mathematics, Science Faculty, Firat University, Elazig 23000, Turkey

E-mail Address: minc@firat.edu.tr

Corresponding author.

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Abdullahi Yusuf

Department of Mathematics, Science Faculty, Federal University Dutse, Jigawa 7156, Nigeria

Department of Mathematics, Science Faculty, Firat University, Elazig 23000, Turkey

E-mail Address: yusufabdullahi@fud.edu.ng

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Mustafa Bayram

Department of Computer Engineering, Istanbul Gelisim University, Istanbul, Turkey

E-mail Address: mbayram@gelisim.edu.tr

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, and

Dumitru Baleanu

Department of Mathematics, Science Faculty, Cankaya University, Ankara 06010, Turkey

Institute of Space Sciences, Magurele 077126, Romania

E-mail Address: dumitru@cankaya.edu.tr

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https://doi.org/10.1142/S0217984919500350Cited by:10 (Source: Crossref)

Abstract

In this paper, symmetry analysis is performed for the nonlinear Chen–Lee–Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.

Keywords:

References

1. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 1995). Google Scholar
2. A. Hesegawa and Y. Kodama, Solitons in Optical Communication (Oxford University Press, Oxford, 1995). Crossref, Google Scholar
3. G. B. Whitham, Linear and Nonlinear Waves (John Wiley, New York, 1974). Google Scholar
4. H. Yilmaz, J. Nonlinear Math. Phys. 22 (2015) 32. Crossref, Web of Science, Google Scholar
5. J. Zhang, W. Liu, D. Qiu, Y. Zhang, K. Porsezian and J. He, Phys. Scripta 90 (2015) 055207. Crossref, Web of Science, Google Scholar
6. H. Triki, Y. Hamaizi, Q. Zhou, A. Biswas, M. Z. Ullah, S. P. Moshokoa and M. Belic, Optik 157 (2018) 156. Crossref, Web of Science, ADS, Google Scholar
7. H. H. Chen, Y. C. Lee and C. S. Liu, Phys. Scripta 20 (1979) 490. Crossref, Web of Science, ADS, Google Scholar
8. H. Triki, Y. Hamaizi, Q. Zhou, A. Biswas, M. Z. Ullah, S. P. Moshokoa and M. Belic, Optik 155 (2018) 329. Crossref, Web of Science, ADS, Google Scholar
9. H. Triki, Q. Zhou, S. P. Moshokoa, M. Z. Ullah, A. Biswas and M. Belic, Optik 155 (2018) 208. Crossref, Web of Science, ADS, Google Scholar
10. M. Inc, A. I. Aliyu, A. Yusuf and D. Baleanu, Optik 158 (2018) 297. Crossref, Web of Science, ADS, Google Scholar
11. H. Triki, A. T. Rubayyi, Q. Zhou and A. Biswas, Superlattices Microst. 111 (2017) 326. Crossref, Web of Science, ADS, Google Scholar
12. M. Ekici, Q. Zhou, A. Sonmezoglu, S. P. Moshokoa, M. Z. Ullah, A. Biswas and M. Belic, Superlattices Microst. 107 (2017) 254. Crossref, Web of Science, ADS, Google Scholar
13. A. Sonmezoglu, M. Yao, M. Ekici, M. Mirzazadeh and Q. Zhou, Nonlinear Dynam. 88 (2017) 595. Crossref, Web of Science, Google Scholar
14. M. Inc, M. S. Hashemi and A. I. Aliyu, Acta Phys. Pol. A 133 (2018) 1133. Crossref, Web of Science, ADS, Google Scholar
15. A. I. Aliyu, M. Inc, A. Yusuf and D. Baleanu, Symmetry 10 (2018) 341. Crossref, Web of Science, ADS, Google Scholar
16. E. Buhe and G. W. Bluman, J. Math. Phys. 56 (2015) 101501. Crossref, Web of Science, ADS, Google Scholar
17. B. Gao, Waves Random Complex Media 27 (2016) 700. Crossref, Web of Science, ADS, Google Scholar
18. L. L. Feng, S. F. Tian, T. T. Zhang and J. Zhou, Chinese J. Phys. 55 (2017) 996. Crossref, Web of Science, ADS, Google Scholar
19. S. C. Anco and G. W. Bluman, Eur. J. Appl. Math. 13 (2002) 567. Crossref, Web of Science, Google Scholar
20. N. H, Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems, 2nd edn. (China Machine Press, Beijing, 2005). Google Scholar
21. W. Rudin, Principles of Mathematical Analysis, 3rd edn. (China Machine Press, Beijing, 2004). Google Scholar
22. P. Clarkson and M. Kruskal, J. Math. Phys. 30 (1989) 2201. Crossref, Web of Science, ADS, Google Scholar
23. G. W. Bluman and S. C. Anco. Symmetry and Integration Methods for Differential Equations (Springer, New York, 2004). Google Scholar
24. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, (Springer-Verlag, World Publishing Corp., Berlin, 1989). Crossref, Google Scholar
25. A. Biswas, M. Mirzazadeh, M. Eslami, D. Milovic and M. Belic, Frequenz 68 (2014) 525. Crossref, Web of Science, ADS, Google Scholar
26. M. Mirzazadeh, M. Eslami, E. Zerrad, M. F. Mahmood, A. Biswas and M. Belic, Nonlinear Dynam. 81 (2015) 1933. Crossref, Web of Science, Google Scholar
27. Q. Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh and M. Eslami, Nonlinear Dynam. 84 (2016) 1883. Crossref, Web of Science, Google Scholar
28. M. Eslami and M. Mirzazadeh, Nonlinear Dynam. 83 (2016) 731. Crossref, Web of Science, Google Scholar
29. M. Eslami and M. Mirzazadeh, Ocean Eng. 83 (2014) 133. Crossref, Web of Science, Google Scholar
30. H. Triki, T. Ak, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, A. H. Kara and T. Aydemir, Nonlinear Dynam. 89 (2017) 501. Crossref, Web of Science, Google Scholar
31. Q. Zhou, M. Mirzazadeh, E. Zerrad, A. Biswas and M. Belic, J. Mod. Optics 63 (2016) 950. Crossref, Web of Science, ADS, Google Scholar
32. Q. Zhou, A. Sonmezoglu, M. Ekici and M. Mirzazadeh, J. Mod. Optics 64 (2017) 2345. Crossref, Web of Science, ADS, Google Scholar