SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION

Abdullahi Yusuf; Mustafa Inc; Mustafa Bayram

SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION

Abstract

This paper acquires the closed form solutions for the Kudryashov-Sinelshchikov (KS) equation. The Riccati-Bernoulli (RB) sub-ODE method is used to acquire such solitons whose structure include trigonmetric, hyperbolic and algebraic structures. Some interesting figures for the obtained solutions are presented in order to shed light on the characteristics of the solutions.

Keywords

References

[1] D. Bleecker, G. Csordas, Basic Partial Differential Equations, Chapman and Hall, New York, (1995).
[2] L. Lam, Nonlinear Physics for Beginners, World Scientific, Singapore, (1998).
[3] J. D. Logan, An Introduction to Nonlinear Partial Differential Equations, John Wiley, New York, (1994).
[4] A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Leiden, (2002).
[5] M. J. Ablowitz, P. A. Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform. Cambridge: Cambridge University Press, (1990).
[6] I. Haddouche, L. Cherbi, A. Biswas. Highly sensitive optical immunosensor for bacteria detection in water. Optoelectronics and Advanced Materials-Rapid Communications, 11(1-2) (2017) 46-50.
[7] M. Ekici, A. Sonmezoglu, Q. Zhou, SP. Moshokoa, MZ. Ullah, A. Biswas, M. Belic. Optical solitons with dwdm technology and four-wave mixing by extended trial equation method. Superlattices and Microstructures, 107 (2017) 254-266.
[8] A. Ja’afar, M. Jawad, M. Mirzazadeh, Q. Zhou, A. Biswas. Optical solitons with anti-cubic nonlinearity using three integration schemes. Superlattices and Microstructures, 105 (2017) (1-10).

[9] MA. Banaja, AA. Al Qarni, HO. Bakodah, Q. Zhou, SP. Moshokoa, A. Biswas. The investigate of optical solitons in cascaded system by improved adomian decomposition scheme. Optik, 130 (2017) 1107-1114.
[10] H. O. Bakodah, A. A. Al-Qarni, M. A. Banaja, Q. Zhou, S. P. Moshokoa, A. Biswas. Bright and dark thirring optical solitons with improved adomian decomposition scheme. Optik, 130 (2017) 1115-1123.
[11] F. Tchier, A. I. Aliyu, A. Yusuf, M. Inc, Dynamics of solitons to the ill-posed Boussinesq equation, Eur. Phys. J. Plus 132 (2017) 136.
[12] N. A. Kudryashov and D. I. Sinelshchikov, “Nonlinear waves in bubbly liquids with consideration for viscosity and heat, transfer,” Physics Letters A, 374 (2010) 2011.
[13] M. Mirzazadeh, M. Eslami, Exact solutions of the Kudryashov-Sinelshchikov equation and nonlinear telegraph equation via the first integral method, Nonlinear Analysis: Modelling and Control, 17 (2012) 481-488.
[14] P. N. Ryabov, Exact solutions of the Kudryashov-Sinelshchikov equation, Applied Mathematics and Computation, 217 (2010) 3585.
[15] M. Wang, “Exact solutions for a compound KdV-Burgers equation,” Physics Letters A, 213 (1996) 279.
[16] A. M. Wazwaz, “Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations,” Applied Mathematics and Computation, 169 (2005) 639.
[17] Z. Feng, “On travellingwave solutions of the Burgers-Kortewegde-Vries equation,” Nonlinearity, 20 (2007) 343.
[18] X. F. Yang, Z. C. Deng, Y. Wei. Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application. Advances in Difference Equations (2015) (2015) 117.
[19] M. S. M. Shehata. A new solitary wave solution of the perturbed nonlinear Schrodinger equation using a Riccati-Bernoulli Sub-ODE method. International J. Phys. Sci. 11(6) (2016) 80.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Abdullahi Yusuf This is me
0000-0002-8308-7943
Nigeria

Mustafa Inc This is me
0000-0003-4996-8373
Türkiye

Mustafa Bayram This is me
0000-0002-2994-7201
Türkiye

Publication Date

June 1, 2019

Submission Date

November 1, 2018

Acceptance Date

January 3, 2019

Published in Issue

Year 2019 Volume: 37 Number: 2

IZ

https://izlik.org/JA56GB99SR

Cite

RIS / Bibtex

APA

Yusuf, A., Inc, M., & Bayram, M. (2019). SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION. Sigma Journal of Engineering and Natural Sciences, 37(2), 439-444. https://izlik.org/JA56GB99SR

AMA

1.Yusuf A, Inc M, Bayram M. SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION. SIGMA. 2019;37(2):439-444. https://izlik.org/JA56GB99SR

Chicago

Yusuf, Abdullahi, Mustafa Inc, and Mustafa Bayram. 2019. “SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION”. Sigma Journal of Engineering and Natural Sciences 37 (2): 439-44. https://izlik.org/JA56GB99SR.

EndNote

Yusuf A, Inc M, Bayram M (June 1, 2019) SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION. Sigma Journal of Engineering and Natural Sciences 37 2 439–444.

IEEE

[1]A. Yusuf, M. Inc, and M. Bayram, “SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION”, SIGMA, vol. 37, no. 2, pp. 439–444, June 2019, [Online]. Available: https://izlik.org/JA56GB99SR

ISNAD

Yusuf, Abdullahi - Inc, Mustafa - Bayram, Mustafa. “SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION”. Sigma Journal of Engineering and Natural Sciences 37/2 (June 1, 2019): 439-444. https://izlik.org/JA56GB99SR.

JAMA

1.Yusuf A, Inc M, Bayram M. SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION. SIGMA. 2019;37:439–444.

MLA

Yusuf, Abdullahi, et al. “SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION”. Sigma Journal of Engineering and Natural Sciences, vol. 37, no. 2, June 2019, pp. 439-44, https://izlik.org/JA56GB99SR.

Vancouver

1.Abdullahi Yusuf, Mustafa Inc, Mustafa Bayram. SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION. SIGMA [Internet]. 2019 Jun. 1;37(2):439-44. Available from: https://izlik.org/JA56GB99SR