| | | |

## Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods

#### Guldem YILDIZ [1] , Durmus DAGHAN [2]

The non-linear partial differential (2+1) dimensional Breaking Soliton equation is studied
by using the direct integration and homotopy perturbation method. In this study, we use direct
integration to obtain the known solution in the literature in practical and shortest way by assigning
some special values to the constants in the solutions of the (2+1) dimensional Breaking Soliton
equation. We also obtain same type solution for (2+1) dimensional Breaking Soliton equation by
using the homotopy perturbation method with one iteration. Similarly, same type solutions can be
done different methods such as (G'/G)-expansion method.
Breaking Soliton equation, Homotopy Perturbation Method, direct integration
• [1] S. Arbabi, M. Najafi, Soliton solutions of nonlinear evolution equations in mathematical Physics, Optik, 2016, 127 4270–4274.
• [2] F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, Nuovo Cimento B, 1976, 32, 201-242.B, 1976, 32, 201.
• [3] F. Calogero, A. Degasperis, Nonlinear evolution equations solvable by the inverse spectral transform, Nuovo Cimento B, 1977, 39, 1-54.
• [4] B. Tian, K. Zhao, Y. Gao, Symbolic Computation in Engineering: Application to a Breaking Soliton Equation, Letters in Applied and Engineering Sciences, 1997, 35, 1081-1083.
• [5] Z. Yan, H. Zhang, Constructing Families of Soliton-Like Solutions to a (2+l)-Dimensional Breaking Soliton Equation Using Symbolic Computation, Computers and Mathematics with Applications, 2002, 44, 1439-1444.
• [6] X. Geng, C. Cao, Explicit solutions of the 2 + 1-dimensional breaking soliton equation, Chaos, Solitons and Fractals, 2004, 22 683–691.
• [7] J. Mei , H. Zhang, New types of exact solutions for a breaking soliton equation, Chaos, Solitons and Fractals, 2004, 20, 771–777.
• [8] S. Zhang, New exact non-traveling wave and coefficient function solutions of the (2 + 1)-dimensional breaking soliton equations, Physics Letters A, 2007, 368, 470–475.
• [9] S. Zhang, A generalized new auxiliary equation method and its application to the (2 + 1)-dimensional breaking soliton equations, Applied Mathematics and Computation, 2007, 190, 510–516.
• [10] S.-H. Ma, J.-P. Fang, C.-L. Zheng, New exact solutions of the (2 + 1)-dimensional breaking soliton system via an extended mapping method, Chaos, Solitons and Fractals, 2009, 40, 210–214.
• [11] Z-L. Tao, Solving the breaking soliton equation by He's variational method, Computers and Mathematics with Applications, 2009, 58, 2395-2397.
• [12] X. Da-Quan, Symmetry reduction and new non-traveling wave solutions of (2 + 1)-dimensional breaking soliton equation, Commun Nonlinear Sci Numer Simulat, 2009, 15, 2061–2065.
• [13] Z. Zhao, Z. Dai, G. Mu, The breather-type and periodic-type soliton solutions for the (2 + 1)-dimensional breaking soliton equation, Computers and Mathematics with Applications, 2011, 61, 2048–2052.
• [14] H. Li, X. Wan, Z. Fu, and S. Liu, New special structures to the (2 + 1)-dimensional breaking soliton equations, Phys. Scr., 2011, 84, 035005 (5pp).
• [15] E. Zayed, M. Abdelaziz, M. Elmalky, Enhanced (G'/G) -Expansion Method and Applications to the (2 + 1) D Typical Breaking Soliton and Burgers Equations, J. Adv. Math. Stud., 2011, 4, 109-122.
• [16] M.T. Darvishi, M. Najafi, Some exact solutions of the (2 + 1)-dimensional break-ing soliton equation using the three-wave method, World Acad. Sci. Eng.Technol., 2011, 55, 919–922.
• [17] M. T. Darvishi, M. Najafi, Some exact solutions of the (2+1)-dimensional breaking soliton equation using the three-wave method, International Journal of Computational and Mathematical Sciences, 2012, 6, 13-16.
• [18] G. Xu, Integrability of a (2+1)-dimensional generalized breaking soliton equation, Applied Mathematics Letters, 2015, 50, 16,22.
• [19] He, JH.: Homotopy perturbation technique, Comp. Meth. Appl. Mech. Eng., 1999, 178, 257-262.
• [20] He, JH.: A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int J Nonlinear Mech, 2000, 35, 37-43.
• [21] He, JH.: Homotopy perturbation method for bifurcation of nonlinear problems, Int J Nonlinear Sci Numer Simul., 2005, 6 (2), 207-208.
• [22] El-Shahed, M.:Application of He’s homotopy perturbation method to Volterra’s integro differential equation, Int J Nonlinear Sci Numer Simul, 2005, 6(2), 163-168.
Primary Language en Engineering, Mathematics Research Article Author: Guldem YILDIZ Author: Durmus DAGHAN Publication Date : May 1, 2016
 Bibtex @research article { jetas281377, journal = {Journal of Engineering Technology and Applied Sciences}, issn = {}, eissn = {2548-0391}, address = {Yıldız Teknik Üniversitesi, Kimya Metalurji Fakültesi, Mathematik Mühendisliği, oda no:A235}, publisher = {Muhammet KURULAY}, year = {2016}, volume = {1}, pages = {13 - 18}, doi = {10.30931/jetas.281377}, title = {Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods}, key = {cite}, author = {Yıldız, Guldem and Daghan, Durmus} } APA Yıldız, G , Daghan, D . (2016). Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods . Journal of Engineering Technology and Applied Sciences , 1 (1) , 13-18 . DOI: 10.30931/jetas.281377 MLA Yıldız, G , Daghan, D . "Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods" . Journal of Engineering Technology and Applied Sciences 1 (2016 ): 13-18 Chicago Yıldız, G , Daghan, D . "Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods". Journal of Engineering Technology and Applied Sciences 1 (2016 ): 13-18 RIS TY - JOUR T1 - Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods AU - Guldem Yıldız , Durmus Daghan Y1 - 2016 PY - 2016 N1 - doi: 10.30931/jetas.281377 DO - 10.30931/jetas.281377 T2 - Journal of Engineering Technology and Applied Sciences JF - Journal JO - JOR SP - 13 EP - 18 VL - 1 IS - 1 SN - -2548-0391 M3 - doi: 10.30931/jetas.281377 UR - https://doi.org/10.30931/jetas.281377 Y2 - 2016 ER - EndNote %0 Journal of Engineering Technology and Applied Sciences Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods %A Guldem Yıldız , Durmus Daghan %T Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods %D 2016 %J Journal of Engineering Technology and Applied Sciences %P -2548-0391 %V 1 %N 1 %R doi: 10.30931/jetas.281377 %U 10.30931/jetas.281377 ISNAD Yıldız, Guldem , Daghan, Durmus . "Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods". Journal of Engineering Technology and Applied Sciences 1 / 1 (May 2016): 13-18 . https://doi.org/10.30931/jetas.281377 AMA Yıldız G , Daghan D . Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods. jetas. 2016; 1(1): 13-18. Vancouver Yıldız G , Daghan D . Solution of the (2+1) Dimensional Breaking Soliton Equation by Using Two Different Methods. Journal of Engineering Technology and Applied Sciences. 2016; 1(1): 13-18.

Authors of the Article
[1]
[2]