Abstract
In this work, Improved Bernoulli Sub-Equation Function (IBSEF) method is proposed to seek solitary solutions of nonlinear differential equations. Chaffee–Infante equations are chosen to illustrate the effectiveness and convenience of the suggested method. Abundant new and more general exact solutions are obtained of these equations. As a result, by selecting the suitable parameters, two and three dimensional surfaces and contour plots of the results are drawn with the help of the software program.
REFERENCES
M. Mirzazadeh, M. Eslami, E. Zerrad, M. F. Mahmood, A. Biswas, and M. Belic, “Optical solitons in nonlinear directional couplers by sine-cosine function method and Bernoulli’s equation approach,” Nonlinear Dyn. 81, 1933–1949 (2015).
R. Sassaman and A. Biswas, “Topological and non-topological solitons of the Klein–Gordon equations in (1 + 2)-dimensions,” Nonlinear Dyn. 61, 23–28 (2010).
A. Biswas, A. B. Kara, A. H. Bokhari, and F. D. Zaman, “Solitons and conservation laws of Klein–Gordon equation with power law and log law nonlinearities,” Nonlinear Dyn. 73, 2191–2196 (2013).
H. M. Baskonus, H. Bulut, and T. A. Sulaiman, “New complex hyperbolic structures to the Lonngren-wave equation by using sine-Gordon expansion method,” Appl. Math. Nonlinear Sci. 4 (1), 129–138 (2019).
H. Durur and A. Yokuş, “Exact solutions of the Benney–Luke equation via (1/G')-expansion method,” BSEU J. Sci. 8 (1), 56–64 (2021).
M. Al Ghabshi, E. V. Krishnan, and M. Alquran, “Exact solutions of a Klein–Gordon system by (G'/G)-expansion method and Weierstrass elliptic function method,” Nonlinear Dyn. Syst. Theory 19 (3), 386–395 (2019).
F. Niu, J. Qi, and Z. Zho, “Some methods about finding the exact solutions of nonlinear modified BBM equation,” Math. Probl. Eng. 2021, 5564162 (2021).
E. A. Saied, R. G. Abd El-Rahman, and M. I. Ghonamy, “A generalized Weierstrass elliptic function expansion method for solving some nonlinear partial differential equations,” Comput. Math. Appl. 58 (9), 1725–1735 (2009).
M. Musette and R. Conte, “Riccati pseudopotential of AKNS two-family NLPDES by Painlevé analysis,” Theor. Math. Phys. 99 (3), 738–744 (1994).
G. Hariharan, “Haar wavelet method for solving Cahn–Allen equation,” Appl. Math. Sci. 3 (51), 2523–2533 (2009).
Y. Fu and J. Li, “Exact stationary-wave solutions in the standard model of the Kerr-nonlinear optical fiber with the Bragg grating,” J. Appl. Anal. Comput. 7, 1177–1184 (2017).
Y. Gürefe,"The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative," Rev. Mex. Fís. 66 (6), 771–781 (2020).
H. Bulut and H. F. Ismael, “Exploring new features for the perturbed Chen–Lee–Liu model via (m + 1; \(\frac{1}{{G'}}\))‑expansion method,” Proc. Inst. Math. Mech. Natl. Acad. Sci. Az. 48 (1), 164–173 (2022).
R. Sakthivel and C. Chun, “New soliton solutions of Chaffee–Infante equations using the exp-function method,” Z. Naturforsch. A 65 (3), 197–202 (2010).
Ş. T. Demiray and U. Bayrakci, “Construction of soliton solutions for Chaffee–Infante equation,” Afyon Kocatepe Univ. J. Sci. Eng. 21, 1046–1051 (2021).
Y. Mao, “Exact solutions to (2 + 1)-dimensional Chaffee–Infante equation,” Pramana J. Phys. 91 (9), 4 (2018).
M. Tahir, S. Kumar, H. Rehman, M. Ramzan, A. Hasan, and M. S. Osman, “Exact traveling wave solutions of Chaffee–Infante equation in (2 + 1)-dimensions and dimensionless Zakharov equation,” Math. Methods Appl. Sci. 44, 1500–1513 (2021).
A. Yokuş and H. Bulut, “On the numerical investigations to the Cahn–Allen equation by using finite difference method,” Int. J. Optim. Control: Theor. Appl. 9 (1), 18–23 (2018).
H. Bulut, G. Yel and H. M. Başkonuş, “An application of improved Bernoulli sub-equation function method to the nonlinear time-fractional Burgers equation,” Turk. J. Math. Comput. Sci. 5, 1–7 (2016).
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Demirbilek, U., Mamedov, K.R. Application of IBSEF Method to Chaffee–Infante Equation in (1 + 1) and (2 + 1) Dimensions. Comput. Math. and Math. Phys. 63, 1444–1451 (2023). https://doi.org/10.1134/S0965542523080067
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DOI: https://doi.org/10.1134/S0965542523080067