Research Article
BibTex RIS Cite

Traveling wave solutions of new coupled Konno-Oono equation

Year 2016, Volume: 4 Issue: 2, 296 - 303, 01.03.2016

Md. Abul Bashar Gobinda Mondal Kamruzzaman Khan Ahmet Bekir

Abstract

In this paper, the recently developed tanh-function method and extended tanh-function method are applied to explore the traveling wave solutions of new coupled Konno-Oono equation. We have successfully derived some explicit traveling wave solutions of new coupled Konno-Oono equation.


Keywords

tanh-function method extended tanh-function method new coupled Konno-Oono equation

References

  • J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals 30: 700-708 (2006).
  • M.A. Akbar, NHM. Ali, Exp-function method for Duffing Equation and new solutions of (2+1) dimensional dispersive long wave equations, Progress in Applied Mathematics, 1 (2), 30-42 (2011).
  • H. Naher, A.F. Abdullah, M.A. Akbar,The Exp-function method for new exact solutions of the nonlinear partial differential equations, International Journal of Physical Sciences, 6 (29), 6706-6716 (2011).
  • H. Naher, AF. Abdullah,MA. Akbar, New traveling wave solutions of the higher Dimensional nonlinear partial differential equation by the Exp-function method, Journal of Applied Mathematics, volume 2012, (doi: 10.1155(2012)575387) (2012).
  • A. Bekir, A. Boz, Exact solutions for nonlinear evolution equations using Exp-function method, Physics Letter A, 372, 1619-1625 (2008).
  • R. Hirota, Exact envelope soliton solutions of a nonlinear wave equation, Journal of Mathematical Physics,14, 805-10 (1973).
  • R. Hirota, J. Satsuma, Soliton solutions of a coupled KDV equation, Physics Letter A,85, 404-408 (1981).
  • G. Adomian, Solving frontier problems of physics: The decomposition method, Boston,M A: Kluwer Academic, (1994).
  • M. S. Islam, K. Khan, M. A. Akbar, and A. Mastroberardino, A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations, Royal Society Open Science, 1, 140038 (doi.org/10.1098/rsos.140038) (2014).
  • Sirendaoreji, New exact travelling wave solutions for the Kawahara and modified Kawahara equations, Chaos Solitons Fractals, 19, 147-150 (2004).
  • M. Shakeel, and S. T. Mohyud-Din,A Novel (G’/G)-Expansion Method and its Application to the (3 + 1)-Dimensional Burger’s Equations, International Journal of Applied & Computational Mathematics, 2(1), 13-24 (DOI 10.1007/s40819-015-0039-5), (2016).
  • K. Khan, M. A. Akbar, and H. Koppelaar, Study of Coupled Nonlinear Partial Differential Equations for finding Exact Analytical Solutions. Royal Society Open Science, 2, 140406, (http://dx.doi.org/10.1098/rsos.140406), (2015).
  • K. Khan, and M. A. Akbar, Study of analytical method to seek for exact solutions of variant Boussinesq equations. SpringerPlus, 3,324, (DOI:10.1186/2193-1801-3-324), (2014).
  • M. H. Islam, K. Khan, M. A. Akbar, and M. A. Salam, Exact Traveling Wave Solutions of Modified KdV–Zakharov–Kuznetsov Equation and Viscous Burgers Equation, SpringerPlus, 3,105, (doi:10.1186/2193-1801-3-105), (2014).
  • M. E. Islam, K. Khan, M. A. Akbar and R. Islam, Traveling Wave Solutions Of Nonlinear Evolution Equation Via Enhanced (G’/G)-Expansion Method, GANIT: Journal of Bangladesh Mathematical Society, 33, 83-92, (http://dx.doi.org/10.3329/ganit.v33i0. 17662), (2013).
  • K. Khan, and M. A. Akbar, Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations. Journal of Scientific Research, 6(2), 273-284. (doi.org/10.3329/jsr.v6i2.16671), (2014).
  • M. T. Ahmed, K. Khan and M. A. Akbar, Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via Modified Simple Equation Method. Physical Review & Research International, 3(4), 490-503 (2013).
  • W. Malfliet and W. Hereman, The tanh method: A tool for solving certain classes of Nonlinear Evolution and Wave Equations, Physica Scripta, 54, 563-568 (1996).
  • X. D. Zheng, T. C Xia and H. Q. Zhang, New exact travelling wave solutions for compound KdV-burgers equation in mathematical physics, Appl. Math. E-Note, 2, 45-50 (2002).
  • J. Manafian, M. Lakestani, and A. Bekir, Study of the Analytical Treatment of the (2+1)-Dimensional Zoomeron, the Duffing and the SRLW Equations via a New Analytical Approach. International Journal of Applied & Computational Mathematics, pp1-26, (DOI 10.1007/s40819-015-0058-2), (2015).
  • A M.Wazwaz, The extended tanh method for new soliton solutions for many forms of the fifth-order KdV equations, Applied Mathematics and Computation, 184 (2), 1002–1014, (doi:10.1016/j.amc.2006.07.002), (2007).
  • A M.Wazwaz, New solitary wave solutions to modified forms of Degasperis-Procesi and Camassa-Holm equations, Applied Mathematics and Computation, 186(1),130–141, (doi:10.1016/j.amc.2006.07.092), (2007).
  • M Labidi, H Triki, E V Krishnan and A Biswas, Soliton solutions of the long-short wave equation with power law nonlinearity, Journal of Applied Nonlinear Dynamics 1 (2), 125-140 (2012).

Year 2016, Volume: 4 Issue: 2, 296 - 303, 01.03.2016

Md. Abul Bashar Gobinda Mondal Kamruzzaman Khan Ahmet Bekir

Abstract

References

  • J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals 30: 700-708 (2006).
  • M.A. Akbar, NHM. Ali, Exp-function method for Duffing Equation and new solutions of (2+1) dimensional dispersive long wave equations, Progress in Applied Mathematics, 1 (2), 30-42 (2011).
  • H. Naher, A.F. Abdullah, M.A. Akbar,The Exp-function method for new exact solutions of the nonlinear partial differential equations, International Journal of Physical Sciences, 6 (29), 6706-6716 (2011).
  • H. Naher, AF. Abdullah,MA. Akbar, New traveling wave solutions of the higher Dimensional nonlinear partial differential equation by the Exp-function method, Journal of Applied Mathematics, volume 2012, (doi: 10.1155(2012)575387) (2012).
  • A. Bekir, A. Boz, Exact solutions for nonlinear evolution equations using Exp-function method, Physics Letter A, 372, 1619-1625 (2008).
  • R. Hirota, Exact envelope soliton solutions of a nonlinear wave equation, Journal of Mathematical Physics,14, 805-10 (1973).
  • R. Hirota, J. Satsuma, Soliton solutions of a coupled KDV equation, Physics Letter A,85, 404-408 (1981).
  • G. Adomian, Solving frontier problems of physics: The decomposition method, Boston,M A: Kluwer Academic, (1994).
  • M. S. Islam, K. Khan, M. A. Akbar, and A. Mastroberardino, A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations, Royal Society Open Science, 1, 140038 (doi.org/10.1098/rsos.140038) (2014).
  • Sirendaoreji, New exact travelling wave solutions for the Kawahara and modified Kawahara equations, Chaos Solitons Fractals, 19, 147-150 (2004).
  • M. Shakeel, and S. T. Mohyud-Din,A Novel (G’/G)-Expansion Method and its Application to the (3 + 1)-Dimensional Burger’s Equations, International Journal of Applied & Computational Mathematics, 2(1), 13-24 (DOI 10.1007/s40819-015-0039-5), (2016).
  • K. Khan, M. A. Akbar, and H. Koppelaar, Study of Coupled Nonlinear Partial Differential Equations for finding Exact Analytical Solutions. Royal Society Open Science, 2, 140406, (http://dx.doi.org/10.1098/rsos.140406), (2015).
  • K. Khan, and M. A. Akbar, Study of analytical method to seek for exact solutions of variant Boussinesq equations. SpringerPlus, 3,324, (DOI:10.1186/2193-1801-3-324), (2014).
  • M. H. Islam, K. Khan, M. A. Akbar, and M. A. Salam, Exact Traveling Wave Solutions of Modified KdV–Zakharov–Kuznetsov Equation and Viscous Burgers Equation, SpringerPlus, 3,105, (doi:10.1186/2193-1801-3-105), (2014).
  • M. E. Islam, K. Khan, M. A. Akbar and R. Islam, Traveling Wave Solutions Of Nonlinear Evolution Equation Via Enhanced (G’/G)-Expansion Method, GANIT: Journal of Bangladesh Mathematical Society, 33, 83-92, (http://dx.doi.org/10.3329/ganit.v33i0. 17662), (2013).
  • K. Khan, and M. A. Akbar, Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations. Journal of Scientific Research, 6(2), 273-284. (doi.org/10.3329/jsr.v6i2.16671), (2014).
  • M. T. Ahmed, K. Khan and M. A. Akbar, Study of Nonlinear Evolution Equations to Construct Traveling Wave Solutions via Modified Simple Equation Method. Physical Review & Research International, 3(4), 490-503 (2013).
  • W. Malfliet and W. Hereman, The tanh method: A tool for solving certain classes of Nonlinear Evolution and Wave Equations, Physica Scripta, 54, 563-568 (1996).
  • X. D. Zheng, T. C Xia and H. Q. Zhang, New exact travelling wave solutions for compound KdV-burgers equation in mathematical physics, Appl. Math. E-Note, 2, 45-50 (2002).
  • J. Manafian, M. Lakestani, and A. Bekir, Study of the Analytical Treatment of the (2+1)-Dimensional Zoomeron, the Duffing and the SRLW Equations via a New Analytical Approach. International Journal of Applied & Computational Mathematics, pp1-26, (DOI 10.1007/s40819-015-0058-2), (2015).
  • A M.Wazwaz, The extended tanh method for new soliton solutions for many forms of the fifth-order KdV equations, Applied Mathematics and Computation, 184 (2), 1002–1014, (doi:10.1016/j.amc.2006.07.002), (2007).
  • A M.Wazwaz, New solitary wave solutions to modified forms of Degasperis-Procesi and Camassa-Holm equations, Applied Mathematics and Computation, 186(1),130–141, (doi:10.1016/j.amc.2006.07.092), (2007).
  • M Labidi, H Triki, E V Krishnan and A Biswas, Soliton solutions of the long-short wave equation with power law nonlinearity, Journal of Applied Nonlinear Dynamics 1 (2), 125-140 (2012).
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Md. Abul Bashar This is me

Gobinda Mondal This is me

Kamruzzaman Khan This is me

Ahmet Bekir This is me

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Bashar, M. A., Mondal, G., Khan, K., Bekir, A. (2016). Traveling wave solutions of new coupled Konno-Oono equation. New Trends in Mathematical Sciences, 4(2), 296-303.
AMA Bashar MA, Mondal G, Khan K, Bekir A. Traveling wave solutions of new coupled Konno-Oono equation. New Trends in Mathematical Sciences. March 2016;4(2):296-303.
Chicago Bashar, Md. Abul, Gobinda Mondal, Kamruzzaman Khan, and Ahmet Bekir. “Traveling Wave Solutions of New Coupled Konno-Oono Equation”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 296-303.
EndNote Bashar MA, Mondal G, Khan K, Bekir A (March 1, 2016) Traveling wave solutions of new coupled Konno-Oono equation. New Trends in Mathematical Sciences 4 2 296–303.
IEEE M. A. Bashar, G. Mondal, K. Khan, and A. Bekir, “Traveling wave solutions of new coupled Konno-Oono equation”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 296–303, 2016.
ISNAD Bashar, Md. Abul et al. “Traveling Wave Solutions of New Coupled Konno-Oono Equation”. New Trends in Mathematical Sciences 4/2 (March2016), 296-303.
JAMA Bashar MA, Mondal G, Khan K, Bekir A. Traveling wave solutions of new coupled Konno-Oono equation. New Trends in Mathematical Sciences. 2016;4:296–303.
MLA Bashar, Md. Abul et al. “Traveling Wave Solutions of New Coupled Konno-Oono Equation”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 296-03.
Vancouver Bashar MA, Mondal G, Khan K, Bekir A. Traveling wave solutions of new coupled Konno-Oono equation. New Trends in Mathematical Sciences. 2016;4(2):296-303.