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Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation

Yıl 2010, Cilt: 7 Sayı: 1, - , 01.02.2010

Öz

In this study, we implemented the generalized Jacobi elliptic function method
with symbolic computation to construct periodic and multiple soliton solutions for the
(2+1)-dimensional breaking soliton equation.

Kaynakça

  • [1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • [2] A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • [3] I. Aslan, T. Ozi¸s, Analytic study on two nonlinear evolution equations by using the ( G'/G )- expansion method, Applied Mathematics and Computation 209 (2009), 425–429.
  • [4] I. Aslan, T. Ozi¸s, On the validity and reliability of the ( G'/G )- expansion method by using higher-order nonlinear equations, Applied Mathematics and Computation 211 (2009), 531–536.
  • [5] A. Bekir, Application of the ( G'/G )- expansion method for nonlinear evolution equations, Physics Letters A 372 (2008), 3400–3406.
  • [6] M. A. Abdou, S. Zhang, New periodic wave solutions via extended mapping method, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 2–11.
  • [7] X. Zhao, H. Zhi and H. Zhang, Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system, Chaos, Solitons & Fractals 28 (2006), 112–126.
  • [8] Q. Wang, Y. Chen, Z. Hongqing, A new Jacobi elliptic function rational expansion method and its application to (1 + 1)-dimensional dispersive long wave equation, Chaos, Solitons & Fractals 23 (2005), 477–483.
  • [9] Y. Yu, Q. Wang, H. Zhang , The extended Jacobi elliptic function method to solve a generalized Hirota-Satsuma coupled KdV equations, Chaos, Solitons & Fractals 26 (2005), 1415–1421.
  • [10] A. H. Khater, O. H. El-Kalaawy, M.A. Helal, Two new classes of exact solutions for the KdV equation via B¨acklund transformations, Chaos, Solitons & Fractals 12 (1997), 1901–1909.
  • [11] M. L. Wang, Exact solutions for a compound KdV-Burgers equation, Physics Letters A 213 (1996), 279–287.
  • [12] M. L. Wang, Y. Zhou, Z. Li, Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A 216 (1996), 67–75.
  • [13] M. A. Helal, M. S. Mehanna, The tanh method and Adomian decomposition method for solving the foam drainage equation, Applied Mathematics and Computation 190 (2007), 599–607.
  • [14] A. M. Wazwaz, The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations, Computers & Mathematics with Applications 49 (2005), 1101–1112.
  • [15] B. R. Duffy, E. J. Parkes, Travelling solitary wave solutions to a seventh-order generalized KdV equation, Physics Letters A 214 (1996), 271–272.
  • [16] E. J. Parkes, B. R. Duffy, Travelling solitary wave solutions to a compound KdV-Burgers equation, Physics Letters A 229 (1997), 217–220.
  • [17] A. Borhanifar, M. M. Kabir, New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations, Journal of Computational and Applied Mathematics 229 (2009), 158–167.
  • [18] A. M. Wazwaz, Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers-type equations, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 2962–2970.
  • [19] E. Demetriou, N. M. Ivanova, C. Sophocleous, Group analysis of (2+1)- and (3+1)- dimensional diffusion-convection equations, Journal of Mathematical Analysis and Applications 348 (2008), 55–65.
  • [20] Y. Yu, Q. Wang, H. Zhang, The extension of the Jacobi elliptic function rational expansion method, Communications in Nonlinear Science and Numerical Simulation 12 (2007), 702–713.
  • [21] T. Ozi¸s, A. Yıldırım, Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation, Chaos, Solitons & Fractals 38 (2008), 209–212.
  • [22] A. Yıldırım, Application of He’s homotopy perturbation method for solving the Cauchy reaction-diffusion problem, Computers & Mathematics with Applications 57 (2009), 612–618.
  • [23] A. Yıldırım, Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations, Communications in Numerical Methods in Engineering (2008), (in press).
  • [24] T. Ozi¸s, A.Yıldırım, Comparison between Adomian’s method and He’s homotopy perturbation method, Computers & Mathematics with Applications 56 (2008), 1216–1224.
  • [25] A.Yıldırım, An Algorithm for Solving the Fractional Nonlinear Schr¨odinger Equation by Means of the Homotopy Perturbation Method, International Journal of Nonlinear Sciences and Numerical Simulation 10 (2009), 445–451.
  • [26] H. Zhao, H. J. Niu , A new method applied to obtain complex Jacobi elliptic function solutions of general nonlinear equations, Chaos, Solitons & Fractals 41 (2009), 224–232.
  • [27] W. Hereman, M. Takaoka, Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, Journal of Physics A: Mathematical and General 23 (1990), 4805–4822.
  • [28] C. Huai-Tang, Z. Hong-Qing, New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation, Chaos, Solitons & Fractals 20 (2004), 765–769.
  • [29] Y. Chen, Q. Wang, Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation, Chaos, Solitons & Fractals 24 (2005), 745–757.
  • [30] E. Fan, J. Zhang, Applications of the Jacobi elliptic function method to special-type nonlinear equations, Physics Letters A, Volume 305 (2002), 383–392.
  • [31] E. J. Parkes, B. R. Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Computer Physics Communications 98 (1996), 288–300.
  • [32] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Physics Letters A 277 (2000), 212–218.
  • [33] S. A. Elwakil, S. K. El-labany, M. A. Zahran and R. Sabry, Modified extended tanh-function method for solving nonlinear partial differential equations, Physics Letters A 299 (2002), 179–188.
  • [34] X. Zheng, Y. Chen and H. Zhang, Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation, Physics Letters A 311 (2003), 145–157.
  • [35] E. Yomba, Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation, Chaos, Solitons & Fractals 20 (2004), 1135–1139.
  • [36] H. Chen, H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos, Solitons & Fractals 19 (2004), 71–76.
Yıl 2010, Cilt: 7 Sayı: 1, - , 01.02.2010

Öz

Kaynakça

  • [1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • [2] A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • [3] I. Aslan, T. Ozi¸s, Analytic study on two nonlinear evolution equations by using the ( G'/G )- expansion method, Applied Mathematics and Computation 209 (2009), 425–429.
  • [4] I. Aslan, T. Ozi¸s, On the validity and reliability of the ( G'/G )- expansion method by using higher-order nonlinear equations, Applied Mathematics and Computation 211 (2009), 531–536.
  • [5] A. Bekir, Application of the ( G'/G )- expansion method for nonlinear evolution equations, Physics Letters A 372 (2008), 3400–3406.
  • [6] M. A. Abdou, S. Zhang, New periodic wave solutions via extended mapping method, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 2–11.
  • [7] X. Zhao, H. Zhi and H. Zhang, Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system, Chaos, Solitons & Fractals 28 (2006), 112–126.
  • [8] Q. Wang, Y. Chen, Z. Hongqing, A new Jacobi elliptic function rational expansion method and its application to (1 + 1)-dimensional dispersive long wave equation, Chaos, Solitons & Fractals 23 (2005), 477–483.
  • [9] Y. Yu, Q. Wang, H. Zhang , The extended Jacobi elliptic function method to solve a generalized Hirota-Satsuma coupled KdV equations, Chaos, Solitons & Fractals 26 (2005), 1415–1421.
  • [10] A. H. Khater, O. H. El-Kalaawy, M.A. Helal, Two new classes of exact solutions for the KdV equation via B¨acklund transformations, Chaos, Solitons & Fractals 12 (1997), 1901–1909.
  • [11] M. L. Wang, Exact solutions for a compound KdV-Burgers equation, Physics Letters A 213 (1996), 279–287.
  • [12] M. L. Wang, Y. Zhou, Z. Li, Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A 216 (1996), 67–75.
  • [13] M. A. Helal, M. S. Mehanna, The tanh method and Adomian decomposition method for solving the foam drainage equation, Applied Mathematics and Computation 190 (2007), 599–607.
  • [14] A. M. Wazwaz, The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations, Computers & Mathematics with Applications 49 (2005), 1101–1112.
  • [15] B. R. Duffy, E. J. Parkes, Travelling solitary wave solutions to a seventh-order generalized KdV equation, Physics Letters A 214 (1996), 271–272.
  • [16] E. J. Parkes, B. R. Duffy, Travelling solitary wave solutions to a compound KdV-Burgers equation, Physics Letters A 229 (1997), 217–220.
  • [17] A. Borhanifar, M. M. Kabir, New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations, Journal of Computational and Applied Mathematics 229 (2009), 158–167.
  • [18] A. M. Wazwaz, Multiple kink solutions and multiple singular kink solutions for two systems of coupled Burgers-type equations, Communications in Nonlinear Science and Numerical Simulation 14 (2009), 2962–2970.
  • [19] E. Demetriou, N. M. Ivanova, C. Sophocleous, Group analysis of (2+1)- and (3+1)- dimensional diffusion-convection equations, Journal of Mathematical Analysis and Applications 348 (2008), 55–65.
  • [20] Y. Yu, Q. Wang, H. Zhang, The extension of the Jacobi elliptic function rational expansion method, Communications in Nonlinear Science and Numerical Simulation 12 (2007), 702–713.
  • [21] T. Ozi¸s, A. Yıldırım, Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation, Chaos, Solitons & Fractals 38 (2008), 209–212.
  • [22] A. Yıldırım, Application of He’s homotopy perturbation method for solving the Cauchy reaction-diffusion problem, Computers & Mathematics with Applications 57 (2009), 612–618.
  • [23] A. Yıldırım, Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations, Communications in Numerical Methods in Engineering (2008), (in press).
  • [24] T. Ozi¸s, A.Yıldırım, Comparison between Adomian’s method and He’s homotopy perturbation method, Computers & Mathematics with Applications 56 (2008), 1216–1224.
  • [25] A.Yıldırım, An Algorithm for Solving the Fractional Nonlinear Schr¨odinger Equation by Means of the Homotopy Perturbation Method, International Journal of Nonlinear Sciences and Numerical Simulation 10 (2009), 445–451.
  • [26] H. Zhao, H. J. Niu , A new method applied to obtain complex Jacobi elliptic function solutions of general nonlinear equations, Chaos, Solitons & Fractals 41 (2009), 224–232.
  • [27] W. Hereman, M. Takaoka, Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, Journal of Physics A: Mathematical and General 23 (1990), 4805–4822.
  • [28] C. Huai-Tang, Z. Hong-Qing, New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation, Chaos, Solitons & Fractals 20 (2004), 765–769.
  • [29] Y. Chen, Q. Wang, Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation, Chaos, Solitons & Fractals 24 (2005), 745–757.
  • [30] E. Fan, J. Zhang, Applications of the Jacobi elliptic function method to special-type nonlinear equations, Physics Letters A, Volume 305 (2002), 383–392.
  • [31] E. J. Parkes, B. R. Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Computer Physics Communications 98 (1996), 288–300.
  • [32] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Physics Letters A 277 (2000), 212–218.
  • [33] S. A. Elwakil, S. K. El-labany, M. A. Zahran and R. Sabry, Modified extended tanh-function method for solving nonlinear partial differential equations, Physics Letters A 299 (2002), 179–188.
  • [34] X. Zheng, Y. Chen and H. Zhang, Generalized extended tanh-function method and its application to (1+1)-dimensional dispersive long wave equation, Physics Letters A 311 (2003), 145–157.
  • [35] E. Yomba, Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation, Chaos, Solitons & Fractals 20 (2004), 1135–1139.
  • [36] H. Chen, H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos, Solitons & Fractals 19 (2004), 71–76.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

İbrahim Enam İnan

Yayımlanma Tarihi 1 Şubat 2010
Yayımlandığı Sayı Yıl 2010 Cilt: 7 Sayı: 1

Kaynak Göster

APA İnan, İ. E. (2010). Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation. Cankaya University Journal of Science and Engineering, 7(1).
AMA İnan İE. Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation. CUJSE. Şubat 2010;7(1).
Chicago İnan, İbrahim Enam. “Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation”. Cankaya University Journal of Science and Engineering 7, sy. 1 (Şubat 2010).
EndNote İnan İE (01 Şubat 2010) Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation. Cankaya University Journal of Science and Engineering 7 1
IEEE İ. E. İnan, “Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation”, CUJSE, c. 7, sy. 1, 2010.
ISNAD İnan, İbrahim Enam. “Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation”. Cankaya University Journal of Science and Engineering 7/1 (Şubat 2010).
JAMA İnan İE. Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation. CUJSE. 2010;7.
MLA İnan, İbrahim Enam. “Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation”. Cankaya University Journal of Science and Engineering, c. 7, sy. 1, 2010.
Vancouver İnan İE. Generalized Jacobi Elliptic Function Method for Traveling Wave Solutions of (2+1)-Dimensional Breaking Soliton Equation. CUJSE. 2010;7(1).