Analytical Solutions of the Nonlinear (2 + 1)-Dimensional Soliton Equation by Using Some Methods

Year 2022, , 141 - 155, 31.08.2022

Ayten Özkan

https://doi.org/10.30931/jetas.1108028

Cited By: 3

Abstract

In this work, it has been applied two methods for solving the (2+1)-dimensional soliton equation, namely, the ansatz method and the F-expansion method. These methods are utilized to provide new accurate periodic and soliton solutions to this problem that are more generic. An appropriate transformation can be used to convert this nonlinear system into another nonlinear ordinary differential equation. In mathematical physics, it is demonstrated that the ansatz method and the F-expansion method give a strong mathematical tool for solving a large number of systems of nonlinear partial differential equations.

Keywords

(2+1)-dimensional soliton equation, the ansatz method, the F-expansion method

References

• [1] Yildirim Y., "Optical solitons of Biswas-Arshed equation by trial equation technique", Optik, 182 (2019) : 876-883.
• [2] Malaikah H. M., "The Adomian decomposition method for solving Volterra-Fredholm integral equation using Maple", Applied Mathematics, 11 (2020) : 779-787.
• [3] Anjum N., He J. H., "Laplace transform: Making the variational iteration method easier", Applied Mathematics Letters, 92 (2019) : 134-138.
• [4] Seadawy A. R., Ali A., Albarakati W.A., "Analytical wave solutions of the(2+1)-dimensional first integro differential Kadomtsev Petviashivili hierarchy equation by using modified mathematical methods", Results in Physics, 15 (2019) : 102775.
• [5] Osman M. S., Baleanu D., Tariq K. U., Kaplan M., Younis M., Rizvi S. T. R., "Different types of progressive wave solutions via the 2D-chiral nonlinear Schrodinger equation", Frontiers in Physics, 8 (2020) : 215.
• [6] Ghanbari B., Inc M., Yusuf A., Baleanu D., "New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics", AIMS Mathematics, 4 (6) (2019) : 1523-1539.
• [7] Ali K. K., Osman M.S., Abdel-Aty M. "New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method", Alexandria Engineering Journal, 59(3) (2020) : 1191-6.
• [8] Kumar V. S., Rezazadeh H., Eslami M., Izadi F., Osman M. S. "Jacobi elliptic function expansion method for solving KdV equation with conformable derivative and dual power law nonlinearity", International Journal of Applied and Computational Mathematics, 5(5) (2019) : 1-10.
• [9] Zahran E. H., "Extended Jacobian elliptic expansion method and its applications in biology", J Appl Math , 6 (2005) : 1174-81.
• [10] Gomez-Aguilar J. F, Osman M. S., Raza N., Zubair A., Arshed S., Ghoneim M. E., Mahmoud E. E., Abdel-Aty A. H., "Optical solitons in birefringent fibers with quadratic cubic nonlinearity using three integration architectures", AIP Adv, 11(2) (2021) : 025121.
• [11] Lu D., Tariq K. U., Osman M. S., Baleanu D., Younis M., Khater M. M., "New analytical wave structures for the (3+ 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications", Results Phys, 14 (2019) : 102491.
• [12] Shakeel M., Din S. T. M., "New -expansion method and its application to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation", Journal of Association of Arab Universities for Basic and Applied Sciences, 18(1) (2015) : 66-81.
• [13] Liu J-G., Osman M. S., Wazwaz A-M., "A variety of non autonomous complex wave solutions for the (2+1)-dimensional nonlinear Schrödinger equation with variable coefficients in nonlinear optical fibers", Optik, 180 (2019) : 917-23.
• [14] Chowdhury M. A., Miah M. M., Ali H. M. S., Chu Y. M., Osman M. S., "An investigation to the nonlinear (2 + 1)-dimensional soliton equation for discovering explicit and periodic wave solutions", Results in Physics 23 (2021) : 104013.
• [15] Yan Z. Y., "Extended Jacobian elliptic function algorithm with symbolic computation to construct new double periodic solutions of nonlinear differential equations", Computer Physics Communications, 148 (2002) : 3042.
• [16] Ye C., Zhang W., "New explicit solutions for (2+1)-dimensional soliton equation", Chaos, Solitons and Fractals, 44 (12) (2011) 1063-1069.
• [17] Arbabi S., Najafi M., Najafi M., "New periodic and soliton solutions of (2 + 1)-dimensional soliton equation", Journal of Advanced Computer Science and Technology, 1 (4) (2012) : 232-239.
• [18] Kumar H., Chand F., "Applications of extended F-expansion and projective Ricatti equation methods to (2+1)-dimensional soliton equations", AIP Advances 3 (2013) : 032128
• [19] Aasaraai A., "The application of modified F-expansion Method solving the Maccari’s system" British Journal of Mathematics & Computer Science, 11 (5) (2015) : 1-14
• [20] Darvishi M. T., Arbabi S., Naja M., Wazwaz A.M., "Traveling wave solutions of a (2+1)-dimensional Zakharov like equation by the first integral method and the tanh method", Optik-International Journal for Light and Electron Optics, 127 (16) (2016) : 6312-6321.
• [21] Mae A., Hassan SZ, "New exact solutions for the Maccari system", J Phys Math 9 (2018) : 264
• [22] Triki, H., Wazwaz, A. M., "Bright and dark soliton solutions for a K(m, n) equation with t-dependent coefficients" Phys. Lett. A. 373, (2009) : 2162-2165.
• [23] Zayed, E. M. E., Amer, Y. A., Shohib, R. M. A., "The Jacobi elliptic function expansion method and its applications for solving the higher order dispersive nonliear Schrödinger equation", Sci. J. Math. Res., 4 (2014) : 53-72.
• [24] Zayed, E. M., Al-Nowehy, A. G., "Exact solutions for the perturbed nonlinear Schrödinger equation with power law nonlinearity and Hamiltonian perturbed terms", Optik, 139 (2017) : 123-144.