The aim of this paper is to investigate the traveling wave solution of the Calogero-Bogoyavlenskii-Schiff (CBS) equation using the Riccati-Bernoulli (RB) sub-ODE method. The (RB) sub-ODE method is used to secure traveling wave solutions that are expressed explicitly and graphically in 3D. The RB sub-ODE technique is a powerful tool that is used to solve various nonlinear partial differential equations (NPDEs). The obtained soliton solutions have been demonstrated by relevant figures.

CBS equation, optical solitons, traveling wave solutions, Riccati-Bernoulli sub-ODE method.

Received: November 10, 2022; Accepted: December 5, 2022; Published: December 21, 2022

How to cite this article: Salisu Ibrahim, Solitary wave solutions for the   (2+1) CBS  equation, Advances in Differential Equations and Control Processes 29 (2022), 117-126. http://dx.doi.org/10.17654/0974324322036

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] G. B. Whitham, Linear and Nonlinear Waves, John Wiley and Sons, 2011.
[2] G. P. Agrawal, Nonlinear fiber optics, Nonlinear Science at the Dawn of the 21st Century, Springer, Berlin, Heidelberg, 2000.
[3] F. Tchier, A. I. Aliyu, A. Yusuf and M. Inc, Dynamics of solitons to the ill-posed Boussinesq equation, The European Physical Journal Plus 132(3) (2017), 1-9.
[4] S. Ibrahim, T. A. Sulaiman, A. Yusuf, A. S. Alshomrani and D. Baleanu, Families of optical soliton solutions for the nonlinear Hirota-Schrodinger equation, Opt. Quant. Electron 54(11) (2022), 1-15. https://doi.org/10.1007/s11082-022-04149-x.
[5] T. A. Sulaiman, A. Yusuf, A. S. Alshomrani and D. Baleanu, Lump collision phenomena to a nonlinear physical model in coastal engineering, Mathematics 10(15) (2022), p. 2805.
[6] J. J. Fang, D. S. Mou, H. C. Zhang and Y. Y. Wang, Discrete fractional soliton dynamics of the fractional Ablowitz-Ladik model, Optik 228 (2021), 166-186.
[7] S. Ibrahim, Discrete least square method for solving differential equations, Advances and Applications in Discrete Mathematics 30 (2022), 87-102. http://dx.doi.org/10.17654/0974165822021.
[8] L. Akinyemi, U. Akpan, P. Veeresha, H. Rezazadeh and M. Inc, Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation, Journal of Ocean Engineering and Science (2022), 1-18. https://doi.org/10.1016/j.joes.2022.02.011.
[9] Y. A. Sabawi, A posteriori error analysis in finite element approximation for fully discrete semilinear parabolic problems, Finite Element Methods and their Applications, IntechOpen, 2020, pp. 1-19.
[10] S. Ibrahim, Numerical approximation method for solving differential equations, Eurasian Journal of Science and Engineering 6(2) (2020), 157-168.
[11] S. Ibrahim and M. E. Koksal, Commutativity of sixth-order time-varying linear systems, Circuits, Systems, and Signal Processing 40(10) (2021), 4799-4832.
[12] S. Ibrahim and M. E. Koksal, Realization of a fourth-order linear time-varying differential system with nonzero initial conditions by cascaded two second-order commutative pairs, Circuits, Systems, and Signal Processing 40(6) (2021), 3107-3123.
[13] S. Ibrahim and A. Rababah, Decomposition of fourth-order Euler-type linear time-varying differential system into cascaded two second-order Euler commutative pairs, Complexity Volume 2022, Article ID 3690019, 9 pp. https://doi.org/10.1155/2022/3690019.
[14] S. Ibrahim, Commutativity of high-order linear time-varying systems, Advances in Differential Equations and Control Processes 27 (2022), 73-83. http://dx.doi.org/10.17654/0974324322013.
[15] S. Ibrahim, Commutativity associated with Euler second-order differential equation, Advances in Differential Equations and Control Processes 28 (2022), 29-36. http://dx.doi.org/10.17654/0974324322022.
[16] X. F. Yang, Z. C. Deng and Y. Wei, A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application, Advances in Difference Equations 2015(1) (2015), 1-17.
[17] D. Baleanu, M. Inc, A. I. Aliyu and A. Yusuf, Dark optical solitons and conservation laws to the resonance nonlinear Schrödinger’s equation with Kerr law nonlinearity, Optik 147 (2017), 248-255.
[18] B. Karaman, New exact solutions of the time-fractional foam drainage equation via a Riccati-Bernoulli sub ode method, Online International Symposium on Applied Mathematics and Engineering (ISAME22), Istanbul-Turkey, 2022, 105 pp.
[19] S. R. Islam, A. Akbulut and S. Y. Arafat, Exact solutions of the different dimensional CBS equations in mathematical physics, Partial Differential Equations in Applied Mathematics 5 (2022), 100320.