Analytical Solutions of Nonlinear Coupled Schrodinger–KdV Equation via Advance Exponential Expansion
American Journal of Mathematical and Computer Modelling
Volume 3, Issue 3, September 2018, Pages: 46-51
Received: Nov. 21, 2018;
Accepted: Dec. 8, 2018;
Published: Feb. 18, 2019
Views 143 Downloads 40
Md. Mashiur Rahhman, Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Ayrin Aktar, Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
Kamalesh Chandra Roy, Department of Mathematics, Begum Rokeya University, Rangpur, Bangladesh
This research work is to represent an advance exp(-Φ(ξ))-expansion method with nonlinear ordinary differential equation for constructing interacting analytical solutions of nonlinear coupled physical models arising in science and engineering. It is capable of determining all branches of interacting analytical solutions simultaneously and this difficult to discriminate with numerical technique. To verify its computational potentiality, the coupled Schrodinger-KdV equation is considered. The obtained solutions in this work reveal that the method is a very effective and easily applicable of formulating the scattered exact traveling wave solutions of many nonlinear coupled wave equations. It is investigated the scattered wave solutions may be useful in understanding the behavior of physical structures in any varied instances, where the coupled Schrodinger-KdV equation is occurred.
Md. Mashiur Rahhman,
Kamalesh Chandra Roy,
Analytical Solutions of Nonlinear Coupled Schrodinger–KdV Equation via Advance Exponential Expansion, American Journal of Mathematical and Computer Modelling.
Vol. 3, No. 3,
2018, pp. 46-51.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Zayed EME. A note on the modified simple equation method applied to Sharma-Tasso-Olver equation. Appl. Math. Comput. 2011; 218 (7); 3962–3964.
Zayed EME and Hoda Ibrahim SA. Modified simple equation method and its applications for some nonlinear evolution equations in mathematical physics. Int. J. Comput. Appli. 2013; 67 (6); 39-44.
Wang ML, Li XZ, Zhang J. The (G'/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 2008; 372; 417-423.
Hafez MG, Alam MN, Akbar MA, Exact traveling wave solutions to the Kelein_Gordon equation using the novel (G'/G)-expansion method, Results in Phys. 2014; 4; 177-184.
Wazwaz AM. The extended tanh-method for new compact and non-compact solutions for the KP-BBM and the ZK-BBM equations. Chaos, Solitons Fract. 2008; 38: 1505-1516.
Malfliet W. The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 2004; 164: 529-541.
Chun C, Sakthivel R. Homotopy perturbation technique for solving two point boundary value problems-comparison with other methods. Computer Phys. Commun. 2010; 181: 1021-1024.
Zhao X, Tang D. A new note on a homogeneous balance method. Phys. Lett. A 2002; 297 (1–2); 59–67.
Zhaosheng F. Comment on the extended applications of homogeneous balance method. Appl. Math. Comput. 2004; 158 (2); 593–596.
Hirota R. Exact solution of the KdV equation for multiple collisions of solutions. Phys. Rev. Lett. 1971; 27; 1192-1194.
Noor MA, Mohyud-Din ST, Waheed A. Exp-function method for travelling wave solutions of nonlinear evolution equations. Appl. Math. Comput. 2010; 216: 477-483.
Noor MA, Mohyud-Din ST, Waheed A. Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations. J. Appl. Math. Computing 2008; 29: 1-13.
Akbar MA, Ali NHM. Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Φ(η)) -expansion method. SpringerPlus, 2014; 3-344. doi: 10.1186/2193-1801-3-344.
Hafez MG, Alam MN, Akbar MA. Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system. J. King Saud Uni.-Sci. in press, 2014. http://dx.doi.org/10.1016/j.jksus.2014.09.001
Hafez MG, Kauser MA, Akter MT. Some new exact traveliing wave solutions of the cubic nonlinear Schrodinger equation using the exp(-Φ(ξ))-expansion method. Int. J. Sci. Eng. Tech. 2014; 3 (7); 848-851.
Hafez MG, Kauser MA, Akter MT. Some new exact travelling wave solutions for the Zhiber-Shabat equation. British J. Math. Com. Sci. 2014; 4 (18); 2582-2593.
Hafez, M. G.: Exact Solutions to the (3+1)-dimensional Coupled Klein-Gordon-Zakharov Equation Using Exp-expansion Method. Alexandria Eng. J. 55, 1635 (2016).
Hafez, M. G., Lu, D.: Traveling Wave Solutions for Space-Time Fractional Nonlinear Evolution Equations. arXiv: 1512.00715 [math. AP] (2015).
Ferdous F, Hafez M G. Oblique closed form solutions of some important fractional evolution equations via the modified Kudryashov method arising in physical problems. Journal of Ocean Engineering and Science 2018; 3: 244.
Ferdous F, Hafez MG,. Ali MY. Obliquely propagating wave solutions to conformable time fractional extended Zakharov–Kuzetsov equation via the generalized exp(−(ξ))-expansion method. SeMA 2018. https://doi.org/10.1007/s40324-018-0164-2
Ferdous F, Hafez MG. Nonlinear time fractional Korteweg-de Vries equations for interaction of wave phenomena in fluid-filled elastic tubes. Eur. Phys. J. Plus 2018; 133: 384.
Lee J, Sakthivel R. Exact travelling wave solutions for some important nonlinear physical models. Pramana - J. Phys. 2013; 80: 757-769.
Jabbari A, Kheiri H, Bekir A. Comput. Math. Appl. 2011; 62: 2177.
Bahrami BS., Abdollahzadeh H, Berijani IM, Ganji DD, Abdollahzadeh M. Pramana – J. Phys. 2011; 77: 263.
Kudryashov NA. A note on the (G'/G)-expansion method. Appl. Math. Comput. 2010; 217 (4): 1755-1758.