New soliton properties to the ill-posed Boussinesq equation arising in nonlinear physical science

Serbay Duran, Muzaffer Askin, Tukur Abdulkadir Sulaiman

Abstract


In manuscript, with the help of the Wolfram Mathematica 9, we employ the modified exponential function method in obtaining some new soliton solutions to the ill-posed Boussinesq equation arising in nonlinear media. Results obtained with use of technique, and also, surfaces for soliton solutions are given. We also plot the 3D and 2D of each solution obtained in this study by using the same program in the Wolfram Mathematica 9.


Full Text:

PDF

References


Akbar, M.A., Ali, N.H.M. and Zayed, E.M.E. (2014). Generalized and Improved -Expansion Method Combined with Jacobi Elliptic Equation, Communications in Theoretical Physics, 61(6), 669.

Parkes, E.J., Duy, B.R. and Abbott, P.C. (2002). The Jacobi Elliptic-Function Method for Finding Periodic-Wave Solutions to Nonlinear Evolution Equations, Physics Letters A, 295, 280-286.

Taghizadeh, N., Mirzazadeh M., Paghaleh, A.S. andVahidi, J. (2012). Exact Solutions of Nonlinear Evolution Equations by Using the Modified Simple Equation Method, Ain Shams Engineering Journal, 3 321-325.

Khan,K.,Akbar, M.A. and Ali, N.H.M. (2013). The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations, Physics Letters A, 2013, 146704.

Baskonus, H.M.,Sulaiman, T.A. and Bulut, H. (2017). On the Novel Wave Behaviors to the Coupled Nonlinear Maccari's System with Complex Structure, Optik, 131, 1036-1043.

Bulut, H., Sulaiman, T.A. and Baskonus, H.M. (2016). New Solitary and Optical Wave Structures to the Korteweg-de Vries Equation with Dual-Power Law Nonlinearity, Opt. Quant. Electron, 48(564), 1-14.

Bulut, H.,Sulaiman, T.A., Baskonus, H.M. and Sandulyak, A.A. (2017). New Solitary and Optical Wave Structures to the (1+1)-Dimensional Combined KdV-mKdV Equation, Optik, 135, 327-336.

Panahipour,H. (2012). Application of Extended Tanh Method to Generalized Burgers-type Equations, Communications in Numerical Analysis, doi:10.5899/2012/cna-00058.

Baskonus, H.M. and Bulut, H. (2016). Exponential Prototype Structure for (2+1)-Dimensional Boiti-Leon-Pempinelli systems in Mathematical Physics, Waves in Random and Complex Media, 26(2), 189-196.

Alquran, M., Al-Khaled, K. and Ananbeh, H. (2011). New Soliton Solutions for Systems of Nonlinear Evolution Equations by the Rational Sine-Cosine Method, Studies in Mathematical Sciences, 3(1), 1-9.

Tchier, F., Yusuf, A., Aliyu, A.I. and Inc, M. (2017). Soliton Solutions and Conservation Laws for Lossy Nonlinear Transmission Line Equation, Superlattices and Microstructures, doi.org/10.1016/j.spmi.2017.04.003.

Hemeda, A.A. (2012). Homotopy Perturbation Method for Solving Systems of Nonlinear Coupled Equations, Applied Mathematical Sciences, 6(96), 4787-4800.

Gao, B. and Tian, H. (2015). Symmetry Reductions and Exact Solutions to the ill-Posed Boussinesq, International Journal of Non-Linear Mechanics, 72, 80-83.

Ozpinar, F., Baskonus, H.M. and Bulut, H. (2015). On the Complex and Hyperbolic Structures for the (2+1)-Dimensional Boussinesq Water Equation, Entropy, 17(12), 8267-8277.

Baskonus, H.M. and Askin, M. (2016). Travelling Wave Simulations to the Modified Zakharov-Kuzentsov Model Arising In Plasma Physics, 6th International Youth Science Forum "LITTERIS ET ARTIBUS"' Computer Science and Engineering, Lviv, Ukraine, 24-26 November.

Boussinesq, J. (1871). Thorie de l'intumescence liquide, applele onde solitaire ou de translation, se propageant dans un canal rectangulaire, Comptes Rendus de l'Academie des Sciences, 72, 755-759.

Zakharov, V.E. (1974). On Stochastization of One-Dimensional Chains of Nonlinear Oscillators, Entropy, 38(1), 108.

Tchier, F., Aliyu, A.I., Yusuf A. and Inc, M. (2017). Dynamics of solitons to the ill-posed Boussinesq equation, The European Physical Journal Plus, 132(136), doi:10.1140/epjp/i2017-11430-0.

Yasar, E., San, S. and Ozkan, Y.S. (2016). Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation, Open Phys., 14, 37-43.

Attili, B.S. (2006). The Adomian Decomposition Methodfor Solving the Boussinesq Equation Arising in Water Wave Propagation, Numerical Methods for Partial Differential Equations, 22, 1337-1347.

Roshid, H.O. and Rahman, M.A. (2014). The exp -expansion method with application in the (1+1) dimensional classical Boussinesq equations, Results Phys., 4, 150-155.

Abdelrahman, A.E., Zahran E.H.M. and Khater, M.M.A. (2015). The exp -Expansion Method and Its Application for Solving Nonlinear Evolution Equations Mahmoud, Int. J. Mod. Nonlinear Theory Appl., 4, 37-47.

Hafez, M.G., Alam, M.N. and Akbar, M.A. (2014). Application of the exp -expansion Method to Find Exact Solutions for the Solitary Wave Equation in an Unmagnatized Dusty Plasma, World Appl. Sci. J., 32, 2150-2155.




DOI: http://dx.doi.org/10.11121/ijocta.01.2017.00495

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Serbay Duran

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

footer_771

   ithe_170     crossref_284         ind_131_43_x_117_117  logo_ehost_120    ulakbim_140   proquest_256_x_97_256   zbmath_251_x_86_251 more...