Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Improved F-Expansion in Mathematical Physics

Year 2020, Volume: 3 Issue: 3, 115 - 123, 29.09.2020

Md. Habibul BASHAR Mamunur ROSHİD

https://doi.org/10.33434/cams.659225

Cited By: 3

Abstract

With the assistance of representative calculation programming, the present paper examines the careful voyaging wave arrangements from the general (2+1)-dimensional nonlinear development conditions by utilizing the Improved F-expansion strategy. As a result, the used technique is effectively utilized and recently delivered some definite voyaging wave arrangements. The recently created arrangements have been communicated as far as trigonometric and hyperbolic capacities. The created arrangements have been returned into their relating condition with the guide of emblematic calculation programming Maple. Among the produced solutions, some solutions have been visualized by 3D and 2D line graphs under the choice of suitable arbitrary parameters to show their physical interpretation. The delivered arrangements show the intensity of the executed technique to evaluate the accurate arrangements of the nonlinear (2+1)-dimensional nonlinear advancement conditions, which are reasonably pertinent for using nonlinear science, scientific material science and designing. The Improved F-expansion method is a reliable treatment for searching essential nonlinear waves that enrich a variety of dynamic models that arise in engineering fields.

Keywords

The Improve F-expansion scheme, Traveling wave solutions, the general (2+1 )-dimensional nonlinear evolution equation

References

• [1] M.O. Al-Amr, Exact solutions of the generalized (2+1)-dimensional nonlinear evolution equations via the modified simple equation method, Comput. Math. Appl, 69(5) (2015), 390-397.
• [2] M. Najafi, S. Arbabi, New Exact Solutions for the Generalized (2+1)-dimensional Nonlinear Evolution Equations by Tanh-Coth Method,. Int. J. Modern Theoretical Phys., 2(2) (2013), 79-85.
• [3] M. Najafi, S. Arbabi, M. Najafi, New application of sine-cosine method for the generalized (2+ 1) dimensional nonlinear evolution equations, Int. J. Adv. Math. Sci.,1(2) (2013), 45-49.
• [4] M. Darvishi, M. Najafi, M. Najafi, New application of EHTA for the generalized (2+ 1)- dimensional nonlinear evolution equations, Int. J. Math. Comp. Sci., 6(3) (2010), 132-138.
• [5] O. I. Bogoyavlenskii, Overturning solitons in new two-dimensional integrable equations, Mathematics of the USSRIzvestiya, 34(2) (1990), 245-259.
• [6] A. M. Wazwaz, New solutions of distinct physical structures to high-dimensional nonlinear evolution equations, Applied Mathematics and Computation, 196 (2008), 363-370.
• [7] Y. Peng, New types of localized coherent structures in the Bogoyavlenskii-Schiff equation,Int. J. Theor. Phys., 45(9) (2006), 1779-1783.
• [8] T. Kobayashi, K. Toda, The Painleve test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients, Symmetry, Inerrability and Geometry,Methods and Applications, 2 (2006),1-10.
• [9] M. S. Bruzon, M. L. Gandarias, C. Muriel, J. Rami rez, S. Saez, F. R. Romero, The Calogero-Bogoyavlenskii-Schiff equation in (2 +1)-dimensions,Theoretical and Mathematical Physics, 137(1) (2003), 1367-1377.
• [10] M. L. Gandarias, M. S. Bruzon, Symmetry group analysis and similarity solutions of the CBS equation in (2+1)-dimensions, Proceedings of Applied Mathematics and Mechanics, 8 (2008), 10591-10592, DOI10.1002/pamm.200810591
• [11] H. P. Zhang, Y. Chen, B. Li, Infinitely many symmetries and symmetry reduction of the (2+1)dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Acta Physica Sinaca, 58 (2009), 7393-7396.
• [12] B. Li, Y. Chen, Exact analytical solutions of the generalized Calogero-Bogoyavlenskii-Schiff equation using symbolic computation, Czechoslovak Journal of Physics, 54 (2004), 517-528.
• [13] J. Wang, X. Yang, Quasi-periodic wave solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (CBS) equation, Nonlinear Analysis, 75 (2012), 2256-2261.
• [14] E. Yasar, Y. Yıldırım, A. Adem, Perturbed optical solitons with spatio-temporal dispersion in (2 + 1)-dimensions by extended Kudryashov method,Optik, 158 (2018), 1–14.
• [15] H. Roshid, M. Roshid, N. Rahman, M. R. Pervin, New solitary wave in shallow water, plasma and ion acoustic plasma via the GZK-BBM equation and the RLW equation,Propulsion and Power Research, 6(1) (2017), 49–57.
• [16] H. Roshid, M. A. Hoque, M. A. Akbar, New extended (G’/G)-expansion method for traveling wave solutions of nonlinear partial differential equations (NPDEs) in mathematical physics,Italian. J. Pure Appl. Math., 33 (2014), 175-190.
• [17] L. Feng, T. Zhang, Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrodinger equation, Appl. Math. Lett., 78(2018), 133-140.
• [18] X. Shuwei, H. Jingsong,The rogue wave and breather solution of the Gerdjikov-Ivanov equation,J. Math. Phys. 53 (2012).
• [19] A. Biswas, M. Mirzazadeh, M. Eslami, Q. Zhou, A. Bhrawy, M. Belic,. Optical solitons in nano-fibers with spatio-temporal dispersion by trial solution method, Optik, 127(18) (2016), 7250–7257.
• [20] J. Heris, I. Zamanpour,Analytical treatment of the Coupled Higgs Equation and the Maccari System via Exp-Function Method,Acta Universitatis Apulensis, 33 (2013), 203-216.
• [21] Y. Zhao,New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method,Journal of Applied Mathematics,(2014), 1-13.
• [22] M. Islam, H. Roshid,Application of -expansion method for Tzitzeica type nonlinear evolution equations,Journal for Foundations and Applications of Physics, 4 (1) (2017).
• [23] N. Rahman, S. Akter,H. Roshid,M. Alam,Traveling Wave Solutions of The (1+1)-Dimensional Compound KdVB equation by $\exp ( - \phi (\xi ))$ –Expansion Method,Global Journal of Science Frontier Research, 13 (8) (2014), 7-13.
• [24] R. Islam, M. Alam, A. Hossain, H. Roshid, M. Akbar, Traveling wave solutions of nonlinear evolution equations via $\exp ( - \phi (\xi ))$ –Expansion Method,Global Journal of Scientific Frontier Research, 13 (11) (2014), 63-71.
• [25] N. Kadkhoda, H. Jafari,Analytical solutions of the Gerdjikov–Ivanov equation by using $\exp ( - \phi (\xi ))$–expansion method,Optik, 139 (2017), 72–76.
• [26] B. Amfilokhiev, I. Voitkunskii, P. Mazaeva, S. Khodorkovskii,Flows of polymer solutions in the case of convective accelerations,Tr. Leningr. Korablestroit. Inst., 96 (1975),3-9.
• [27] M. Roshid,H. Roshid, Exact and explicit traveling wave solutions to two nonlinear evolution equations which describe incompressible viscoelastic Kelvin-Voigt fluid,Heliyon, 4 (2018).
• [28] O. Gozukızıl, S. Akcagıl, The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutions, Advances in Difference Equations, 143 (2013).
• [29] A. Turgut, T. Aydemir, A. Saha, A. Kara, Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation,Pramana – J. Phys., (2018), 78-90.
• [30] J.L.G Guirao .,H. M. Baskonus , A. Kumar, M.S. Rawat , G. Yel, Complex Patterns to the (3+1)-Dimensional B-type Kadomtsev-Petviashvili-Boussinesq Equation, Symmetry, 12(1) (2020).
• [31] W. Gao, G. Yel,H. M. Baskonus, C. Cattani, Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup- Newell-Segur equation, Aims Math., 5(1) (2020), 507–521.
• [32] W. Gao, H. F. Ismael, H. Bulut, .H. M Baskonus, Instability modulation for the (2+1)-dimension paraxial wave equation and its new optical soliton solutions in Kerr media, Physica Scripta, (2019),DOI:10.1088/1402-4896/ab4a50.
• [33] W. Gao, M. Partohaghighi, H. M. Baskonus, S. Ghavi, Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model,Results Phys., 15 (102555) (2019), 1-7.
• [34] H. M. Baskonus, S. Ghavi, New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with MM-derivative,Modern Phys. Letters B, 33(21) (2019), 1950251-(1-16).
• [35] H. M. Baskonus, Complex Soliton Solutions to the Gilson–Pickering Model, Axioms, 8(1) (2019), 18.
• [36] O.A. Ilhan , A. Esen, H. Bulut, H. M. Baskonus, Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves, Results Phys , 12 (2019), 1712–1715.
• [37] G. Yel, H. M. Baskonus, H. Bulut, Regarding some novel exponential travelling wave solutions to the Wu–Zhang system arising in nonlinear water wave model, Indian J. Phys., 93(8) (2019), 1031–1039.
• [38] A. Yokus, Numerical solution for space and time fractional order Burger type equation, Alexandria Eng. J. 57(3) (2018), 2085-2091.