Research Article
BibTex RIS Cite
Year 2022, , 99 - 104, 01.12.2022
https://doi.org/10.33187/jmsm.1123178

Abstract

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.

Novel Solutions of Perturbed Boussinesq Equation

Year 2022, , 99 - 104, 01.12.2022
https://doi.org/10.33187/jmsm.1123178

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.

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.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Şeyma Tülüce Demiray 0000-0002-8027-7290

Uğur Bayrakcı 0000-0002-1765-2318

Publication Date December 1, 2022
Submission Date May 30, 2022
Acceptance Date September 28, 2022
Published in Issue Year 2022

Cite

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 Tülüce Demiray Ş, Bayrakcı U. Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling. December 2022;5(3):99-104. doi:10.33187/jmsm.1123178
Chicago Tülüce Demiray, Şeyma, and Uğur Bayrakcı. “Novel Solutions of Perturbed Boussinesq Equation”. Journal of Mathematical Sciences and Modelling 5, no. 3 (December 2022): 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 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, 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 2022), 99-104. https://doi.org/10.33187/jmsm.1123178.
JAMA 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, 2022, pp. 99-104, doi:10.33187/jmsm.1123178.
Vancouver Tülüce Demiray Ş, Bayrakcı U. Novel Solutions of Perturbed Boussinesq Equation. Journal of Mathematical Sciences and Modelling. 2022;5(3):99-104.

29237    Journal of Mathematical Sciences and Modelling 29238

                   29233

Creative Commons License The published articles in JMSM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.