Applications of the Sub Equation Method for the High Dimensional Nonlinear Evolution Equation

Year 2021, Volume: 14 Issue: 3, 898 - 906, 18.12.2021

Serbay Duran , Doğan Kaya

https://doi.org/10.18185/erzifbed.881743

Cited By: 2

Abstract

In this article, Generalized (3+1)-dimensional Shallow Water-Like (SWL) equation is taken into consideration and exact solutions have been constructed of the SWL equation using sub equation method. This method is an easier and efficient method for finding analytic solutions of nPDEs. The method appears to be easier and faster for symbolic computation. Moreover 2D, 3D and contour graphical representation of the obtained results of the specified equation is made using ready-made package program for certain values and thus the conformity of the founded results has been demonstrated.

Keywords

sub equation method, the Generalized (3+1)-dimensional Shallow Water-Like equation, exact solution, traveling wave solution

References

• Benetazzo, A., Barbariol, F., Pezzutto, P., Staneva, J., Behrens, A., Davison, S., & Cavaleri, L. (2021). “Towards a unified framework for extreme sea waves from spectral models: Rationale and applications”, Ocean Engineering, 219, 108263.
• Gao, W., H. M. Baskonus, and L. Shi. 2020. “New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019-nCoV system”, Advances in Difference Equations (1): 1-11.
• Yavuz, M., & Yokus, A. (2020). “Analytical and numerical approaches to nerve impulse model of fractional‐order”, Numerical Methods for Partial Differential Equations, 36(6), 1348-1368.
• Yokus, A., & Yavuz, M. (2020). Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete & Continuous Dynamical Systems-S.
• Eckart, C. (1948). “Vortices and streams caused by sound waves”, Physical review, 73(1), 68.
• Baskonus, H. M., H. Bulut, and T. A. Sulaiman. 2019. “New complex hyperbolic structures to the lonngren-wave equation by using sine-gordon expansion method”. Applied Mathematics and Nonlinear Sciences, 4 (1): 129-138.
• Fellmann, E. A. (2007). “Leonhard Euler”, Springer Science & Business Media.
• Bona, J. L., & Sachs, R. L. (1988). “Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation”, Communications in mathematical physics, 118(1), 15-29.
• Duran, S., Askin, M., & Sulaiman, T. A. (2017). “New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science”, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(3), 240-247.
• Ahmad, H., Khan, T. A., Durur, H., Ismail, G. M., & Yokus, A. (2020). “Analytic approximate solutions of diffusion equations arising in oil pollution”, Journal of Ocean Engineering and Science, 6(1), 62-69.
• Yokuş, A., Durur, H., Nofal, T. A., Abu-Zinadah, H., Tuz, M., & Ahmad, H. (2020). “Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation”, Open Physics, 18(1), 1003-1010.
• Russell, J. S. (1845). “Report on Waves”, Made to the Meetings of the British Association in 1842-43.
• Scott, A. C., Chu, F. Y. F., & McLaughlin, D. W. (1973). “The soliton: A new concept in applied science”, Proceedings of the IEEE, 61(10), 1443-1483.
• Bulut, H., Atas, S. S., & Baskonus, H. M. (2016). “Some novel exponential function structures to the Cahn–Allen equation”, Cogent Physics, 3(1), 1240886.
• Baskonus, H. M., & Bulut, H. (2015). “On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method”, Waves in Random and Complex Media, 25(4), 720-728.
• Silambarasan, R., & Kilicman, A. (2021). “Solitons of nonlinear dispersive wave steered from Navier-Bernoulli hypothesis and Love's hypothesis in the cylindrical elastic rod with compressible Murnaghan's materials”, arXiv preprint arXiv:2101.05070.
• Ali, K. K., Seadawy, A. R., Yokus, A., Yilmazer, R., & Bulut, H. (2020). “Propagation of dispersive wave solutions for (3+ 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics”, International Journal of Modern Physics B, 34(25), 2050227.
• Yokus, A., Durur, H., Ahmad, H., & Yao, S. W. (2020). “Construction of different types analytic solutions for the Zhiber-Shabat equation”, Mathematics, 8(6), 908.
• Durur, H. (2020). “Different types analytic solutions of the (1+1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method”, Modern Physics Letters B, 34 (03), 2050036.
• Durur, H., and A. Yokuş, and D. Kaya. (2020). “Hyperbolic Type Traveling Wave Solutions of Regularized Long Wave Equation”, Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7 (2).
• Dusunceli, F. (2019). “Exact Solutions for Generalized (3+ 1)-Dimensional Shallow Water-Like (SWL) Equation”, In Conference Proceedings of Science and Technology, 2(1), 55-57.
• Tian, B., & Gao, Y. T. (1996). “Beyond travelling waves: a new algorithm for solving nonlinear evolution equations”, Computer Physics Communications, 95(2-3), 139-142.
• Zayed, E. M. E. (2010). “Traveling wave solutions for higher dimensional nonlinear evolution equations using the g’/g-expansion method”, Journal of Applied Mathematics & Informatics, 28(1_2), 383-395.
• Ya-Ning, T., Wen-Xiu, M., & Wei, X. (2012). “Grammian and Pfaffian solutions as well as Pfaffianization for a (3+ 1)-dimensional generalized shallow water equation”, Chinese Physics B, 21(7), 070212.
• Zhang, Y., Dong, H., Zhang, X., & Yang, H. (2017). “Rational solutions and lump solutions to the generalized (3+ 1)-dimensional shallow water-like equation”, Computers & Mathematics with Applications, 73(2), 246-252.
• Durur, H., Kurt, A., & Tasbozan, O. (2020). “New travelling wave solutions for KdV6 equation using sub equation method”, Applied Mathematics and Nonlinear Sciences, 5(1), 455-460.