Abundant travelling wave solutions of 3+1 dimensional Boussinesq equation with dual dispersion

Authors

  • Sait SAN Eskis¸ehir Osmangazi University
  • R. Altunay Eskis¸ehir Osmangazi University

DOI:

https://doi.org/10.31349/RevMexFisE.19.020203

Keywords:

Jacobi elliptic function method, solitary wave solutions, exact solutions

Abstract

This study presents utilization of Jacobi elliptic function expansion method to obtain the di¤erent types solutions of 3+1
dimensional Boussinesq equation with dual dispersion. By using this method hyperbolic solutions and trigonometric function
solutions are also obtained. The resulting outcomes verify that the preferred method is valid and reliable for the analytical technique of an extensive application of nonlinear phenomena.

References

Wazwaz, A-M. "A sine-cosine method for handlingnonlinear wave equations." Mathematical and Computer mod-

elling 40.5-6 (2004): 499-508.

Alquran, Marwan, and Kamel Al-Khaled. "The tanh and sinecosine methods for higher order equations of

Kortewegde Vries type." Physica Scripta 84.2 (2011): 025010.

Arshad, M., Seadawy, A. R., Lu, D., & Saleem, M. S. (2021). Elliptic function solutions, modulation instability

and optical solitons analysis of the paraxial wave dynamical model with Kerr media. Optical and Quantum

Electronics, 53(1), 1-20.

Çelik, N., Seadawy, A. R., Özkan, Y. S., & Ya¸sar, E. A model of solitary waves in a nonlinear elastic circular rod:

Abundant di¤erent type exact solutions and conservation laws. Chaos, Solitons & Fractals, 143, 110486.

Jhangeer, A., Raza, N., Rezazadeh, H., & Seadawy, A. (2020). Nonlinear self-adjointness, conserved quantities,

bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model. Pramana,

(1), 1-9.

Shukri, Sami, and Kamel Al-Khaled. "The extended tanh method for solving systems of nonlinear wave equations."

Applied Mathematics and Computation 217.5 (2010): 1997-2006.

Farah, N., Seadawy, A. R., Ahmad, S., Rizvi, S. T. R., & Younis, M. (2020). Interaction properties of soliton

molecules and Painleve analysis for nano bioelectronics transmission model. Optical and Quantum Electronics,

(7), 1-15.

Rizvi, S. T., Seadawy, A. R., Ali, I., & Younis, M. (2020). Painlevé analysis of a nonlinear Schrödinger equation

discussing dynamics of solitons in optical ber. International Journal of Modern Physics B, 2150005.

Alquran, Marwan, Mohammed Ali, and Kamel Al-Khaled. "Solitary wave solutions to shallow water waves arising

in uid dynamics." Nonlinear Studies 19.4 (2012): 555-562.

Akram, U., Seadawy, A. R., Rizvi, S. T. R., Younis, M., & Zahed, H. (2020). Travelling wave solutions for the

fractional Wazwaz-Benjamin-Bona-Mahony model in arising shallow water waves. Results in Physics, 103725.

Vakhnenko, V. O., E. J. Parkes, and A. J. Morrison. "A Bäcklund transformation and the inverse scattering

transform method for the generalised Vakhnenko equation." Chaos, Solitons & Fractals 17.4 (2003): 683-692.

Jafari, H., H. Tajadodi, and D. Baleanu. "Application of a homogeneous balance method to exact solutions of

nonlinear fractional evolution equations." Journal of Computational and Nonlinear Dynamics 9.2 (2014): 021019.

Weiss, John. "The Painlevé property for partial di¤erential equations. II: Bäcklund transformation, Lax pairs,

and the Schwarzian derivative." Journal of Mathematical Physics 24.6 (1983): 1405-1413.

Ali, A., & Seadawy, A. R. (2020). Dispersive soliton solutions for shallow water wave system and modi ed

Benjamin-Bona-Mahony equations via applications of mathematical methods. Journal of Ocean Engineering and

Science.

Zhang, Sheng. "Application of Exp-function method to a KdV equation with variable coe¢ cients." Physics Letters

A 365.5-6 (2007): 448-453.

Ali, Ahmad T. "New generalized Jacobi elliptic function rational expansion method." Journal of computational

and applied mathematics 235.14 (2011): 4117-4127.

Novikov, S., et al. Theory of solitons: the inverse scattering method. Springer Science & Business Media, 1984.

Kudryashov, Nikolai A., and Nadejda B. Loguinova. "Extended simplest equation method for nonlinear di¤erential

equations." Applied Mathematics and Computation 205.1 (2008): 396-402.

Maliet, Willy, and Willy Hereman. "The tanh method: I. Exact solutions of nonlinear evolution and wave

equations." Physica Scripta 54.6 (1996): 563.

Hong-Cai, Ma. "A simple method to generate Lie point symmetry groups of the (3+ 1)-dimensional JimboMiwa

equation." Chinese Physics Letters 22.3 (2005): 554.

Cherruault, Y., M. Inc, and K. Abbaoui. "On the solution of the non-linear Kortewegde Vries equation by the

decomposition method." Kybernetes 31.5 (2002): 766-772.

Ünsal, Ömer, and Filiz Ta¸scan. "Soliton solutions, Bäcklund transformation and Lax pair for coupled Burgers

system via Bell polynomials." Zeitschrift für Naturforschung A 70.5 (2015): 359-363.

Chen, Jian-hong, and Wen-shan Duan. "Instability of waves in magnetized vortex-like ion distribution dusty

plasmas." Physics of Plasmas 14.8 (2007): 083702.

Senthilvelan, M. "On the extended applications of homogenous balance method." Applied Mathematics and

Computation 123.3 (2001): 381-388.

Allen, M. A., and G. Rowlands. "On the transverse instabilities of solitary waves." Physics Letters A 235.2 (1997):

-146.

Chen, Yong, Zhenya Yan, and Honging Zhang. "New explicit solitary wave solutions for (2+ 1)-dimensional

Boussinesq equation and (3+ 1)-dimensional KP equation." Physics Letters A 307.2-3 (2003): 107-113.

Yong-Qi, Wu. "Periodic wave solution to the (3+ 1)-dimensional Boussinesq equation." Chinese Physics Letters

8 (2008): 2739.

Moleleki, Letlhogonolo Daddy, and Chaudry Masood Khalique. "Symmetries, Traveling Wave Solutions, and

Conservation Laws of a-Dimensional Boussinesq Equation." Advances in Mathematical Physics 2014 (2014).

S. K. Liu, Z. T. Fu, S. D. Liu and Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions

of nonlinear wave equations, Phys.Lett.A 289 (2001) pp. 69-74.

Z. T. Fu, S. K. Liu, S. D. Liu and Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions

of nonlinear wave equations , Phys.Lett.A 290 (2001) pp. 72-76.

Seadawy, Aly R., Dianchen Lu, and Mostafa MA Khater. "Bifurcations of solitary wave solutions for the three

dimensional ZakharovKuznetsovBurgers equation and Boussinesq equation with dual dispersion." Optik 143

(2017): 104-114.

Ebaid, Abdelhalim, and Emad H. Aly. "Exact solutions for the transformed reduced Ostrovsky equation via the

The F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions." Wave Motion 49.2 (2012):

-308.

Downloads

Published

2022-04-30

How to Cite

[1]
S. SAN and R. Altunay, “Abundant travelling wave solutions of 3+1 dimensional Boussinesq equation with dual dispersion”, Rev. Mex. Fis. E, vol. 19, no. 2 Jul-Dec, pp. 020203 1–, Apr. 2022.

Issue

Vol. 19 No. 2 Jul-Dec (2022): Revista Mexicana de Física E

Section

02 Education in Physics

License

Copyright (c) 2022 Sait SAN, R. Altunay

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.