SOLITON SOLUTIONS FOR KUDRYASHOV-SINELSHCHIKOV EQUATION

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.

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  • [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.