Novel Solutions of Perturbed Boussinesq Equation

Şeyma Tülüce Demiray; Uğur Bayrakcı

doi:10.33187/jmsm.1123178

EN

Novel Solutions of Perturbed Boussinesq Equation

Abstract

In this article, we have worked on the perturbed Boussinesq equation. We have applied the generalized Kudryashov method (GKM) and sine-Gordon expansion method (SGEM) to the perturbed Boussinesq equation. So, we have obtained some new soliton solutions of the perturbed Boussinesq equation. Furthermore, we have drawn some 2D and 3D graphics of these results by using Wolfram Mathematica 12.

Keywords

Generalized Kudryashov method, Perturbed Boussinesq equation, Sine-Gordon expansion method, Soliton solutions

References

[1] A. R. Seadawy, N. Cheemaa, Applications of extended modified auxiliary equation mapping method for high-order dispersive extended nonlinear Schr¨odinger equation in nonlinear optics, Mod. Phys. Lett. B, 33(18) (2019), 1-11.
[2] F. Düşünceliceli, E. Çelik, M. As¸kın, H. Bulut, New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method, Indian J. Phys., 95(2) (2021), 309-314.
[3] S. Chettouh, H. Triki, A. El-Akrmi, Q. Zhou, S. P. Moshokoa, M. Z. Ullah, A. Biswas, M. Belic, Dipole solitons in an extended nonlinear Schr¨odinger’s equation with higher-order even and odd terms, Optik, 145 (2017), 644-649.
[4] M. A. Akbar, N. H. M. Ali, The improved F-expansion method with Riccati equation and its applications in mathematical physics, Cogent Math., 4(1) (2017), 1-19.
[5] S. T. R. Rizvi, K. Ali, M. Ahmad, Optical solitons for Biswas-Milovic equation by new extended auxiliary equation method, Optik, 204 (2020), 164181.
[6] M. Tahir, A. U. Awan, Optical singular and dark solitons with Biswas-Arshed model by modified simple equation method, Optik, 202 (2020), 163523.
[7] Y. Gürefe, E. Mısırlı, Y. Pandır, A. S¨onmezo˘glu, M. Ekici, New exact solutions of the Davey-Stewartson equation with power-law nonlinearity, Bull. Malays. Math. Sci. Soc., 4 (2015), 1223-1234.
[8] A. Akbulut, M. Kaplan, F. Tas¸can, The investigation of exact solutions of nonlinear partial diferential equations by using exp(f(x )) method, Optik, 132 (2017), 382-387.
[9] O. Tas¸bozan, Y. C¸ enesiz, A. Kurt, New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method, Eur. Phys. J. Plus., 131(244) (2016), 1-14.
[10] S. Tülüce Demiray, H. Bulut, New exact solutions for generalized Gardner equation, Kuwait J. Sci., 44(1) (2017), 1-8.

[11] S. Tülüce Demiray, H. Bulut, G. Onargan, An application of generalized tanh function method for the sixth-order Boussinesq (sB) equation and (1+1) dimensional dispersive long wave equation, Appl. Math. Sci., 9(16) (2015), 773-790.
[12] O. A.İlhan, H. Bulut, T. A. Sulaiman, H. M. Bas¸konus¸, On the new wave behavior of the Magneto-Electro-Elastic(MEE) circular rod longitudinal wave equation, Optik, 10(1) (2020), 1-8.
[13] G. Ebadi, S. Johnson, E. Zerrad, A. Biswas, Solitons and other nonlinear waves for the perturbed Boussinesq equation with power law nonlinearity, J. King Saud Univ. Sci., 24(3) (2012), 237-241.
[14] M. A. Akbar, N. H. M. Ali, T. Tanjim, Adequate soliton solutions to the perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon equation, J. King Saud Univ. Sci., 342(6) (2020), 2777-2785.
[15] P. Daripa, R. K. Dash, Weakly non-local solitary wave solutions of a singularly perturbed Boussinesq equation, Math. Comput. Simul., 55(4-6) (2002), 393-405.
[16] R. K. Dash, P. Daripa, Analytical and numerical studies of a singularly perturbed Boussinesq equation, Appl. Math. Comput., 126(1) (2002), 1-30.
[17] X. Y. Jiao, Truncated series solutions to the (2+1)-dimensional perturbed Boussinesq equation by using the approximate symmetry method, Chin. Phys. B, 27(10) (2018), 1-7.
[18] S. Tülüce Demiray, U. Bayrakc¸ı, Soliton Solutions of Generalized Third-Order Nonlinear Schr¨odinger Equation by Using GKM, Journal of the Institute of Science and Technology, 11(2) (2021), 1481-1488.
[19] S. Tülüce Demiray, H. Bulut, Soliton solutions of some non-linear evolution problems by GKM, Neural. Comput. Appl., 31 (2019), 287-294.
[20] Y. Pandır, S. Eren, Exact solutions of the two dimensional KdV-Burger equation by generalized Kudryashov method, Journal of the Institute of Science and Technology, 11(1) (2021), 617-624.
[21] S. Tülüce Demiray, H. Bulut, Generalized Kudryashov method for nonlinear fractional double sinh-poisson equation, Journal of Nonlinear Science and Applications, 9 (2016), 1349-1355.
[22] S. Tülüce Demiray, U. Bayrakc¸ı, Construction of soliton solutions for Chaffee-Infante equation, Afyon Kocatepe University Journal of Science and Engineering, 21(5) (2021), 1046-1051.
[23] O. Tas¸bozan, A. Kurt, The new travelling wave solutions of time fractional Fitzhugh-Nagumo equation with Sine-Gordon expansion method, ADYU J. Sci., 10(1) (2020), 256-263.
[24] G. Yel, H. Bulut, E.˙Ilhan, A new analytical method to the conformable chiral nonlinear Schr¨odinger equation in the quantum Hall effect, Pramana, 96 (2022), 54.
[25] K. K. Ali, A. R. Seadawy, A. Yokus¸, R. Yılmazer, H. Bulut, Propagation of dispersive wave solutions for (3+1)-dimensional nonlinear modified Zakharov-Kuznetsov equation in plasma physics, Int. J. Mod. Phys. B, 35(25) (2020), 2050227.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Şeyma Tülüce Demiray
0000-0002-8027-7290
Türkiye

Uğur Bayrakcı ^*
0000-0002-1765-2318
Türkiye

Publication Date

December 1, 2022

Submission Date

May 30, 2022

Acceptance Date

September 28, 2022

Published in Issue

Year 2022 Volume: 5 Number: 3

DOI

https://doi.org/10.33187/jmsm.1123178

IZ

https://izlik.org/JA34ZB55AE

APA

Tülüce Demiray, Ş., & Bayrakcı, U. (2022). Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling, 5(3), 99-104. https://doi.org/10.33187/jmsm.1123178

AMA

1.Tülüce Demiray Ş, Bayrakcı U. Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling. 2022;5(3):99-104. doi:10.33187/jmsm.1123178

Chicago

Tülüce Demiray, Şeyma, and Uğur Bayrakcı. 2022. “Novel Solutions of Perturbed Boussinesq Equation”. Journal of Mathematical Sciences and Modelling 5 (3): 99-104. https://doi.org/10.33187/jmsm.1123178.

EndNote

Tülüce Demiray Ş, Bayrakcı U (December 1, 2022) Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling 5 3 99–104.

IEEE

[1]Ş. Tülüce Demiray and U. Bayrakcı, “Novel Solutions of Perturbed Boussinesq Equation”, Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, pp. 99–104, Dec. 2022, doi: 10.33187/jmsm.1123178.

ISNAD

Tülüce Demiray, Şeyma - Bayrakcı, Uğur. “Novel Solutions of Perturbed Boussinesq Equation”. Journal of Mathematical Sciences and Modelling 5/3 (December 1, 2022): 99-104. https://doi.org/10.33187/jmsm.1123178.

JAMA

1.Tülüce Demiray Ş, Bayrakcı U. Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling. 2022;5:99–104.

MLA

Tülüce Demiray, Şeyma, and Uğur Bayrakcı. “Novel Solutions of Perturbed Boussinesq Equation”. Journal of Mathematical Sciences and Modelling, vol. 5, no. 3, Dec. 2022, pp. 99-104, doi:10.33187/jmsm.1123178.

Vancouver

1.Şeyma Tülüce Demiray, Uğur Bayrakcı. Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling. 2022 Dec. 1;5(3):99-104. doi:10.33187/jmsm.1123178

Cited By

Analysis of perturbed Boussinesq equation via novel integrating schemes

PLOS ONE

https://doi.org/10.1371/journal.pone.0302784

29237 Journal of Mathematical Sciences and Modelling 29238

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