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Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation

Yıl 2019, Cilt: 16 Sayı: 1, 54 - 62, 31.05.2019

Öz


In this paper, we
implemented a tan
 -Expansion Method for some traveling wave solutions
of (3+1)-dimensional Jimbo-Miwa equation.

Kaynakça

  • L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • Y. Shang, Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation, Appl.Math.Comput. 187, (2007), 1286-1297.
  • T. L. Bock, M.D. Kruskal, A two-parameter Miura transformation of the Benjamin-Ono equation, Phys. Lett. A 74, (1979), 173-176.
  • V. B. Matveev, M.A. Salle, Darboux Transformations and Solitons, Springer, Berlin, 1991.
  • A. M. Abourabia, M. M. El Horbaty, On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation, Chaos Solitons Fractals, 29, (2006), 354-364.
  • Y. Chuntao, A simple transformation for nonlinear waves, Phys. Lett. A, 224, (1996), 77-84.
  • F. Cariello, M. Tabor, Painleve expansions for nonintegrable evolution equations, Physica D, 39, (1989), 77-94.
  • E. Fan, Two new application of the homogeneous balance method, Phys. Lett. A, 265, (2000), 353-357.
  • P. A. Clarkson, New similarity solutions for the modified boussinesq equation, J. Phys. A: Math. Gen., 22, (1989), 2355-2367.
  • W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, (1992), 650-654.
  • W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, (1992), 650-654.
  • E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277, (2000), 212-218.
  • S. A. Elwakil, S.K. El-labany, M.A. Zahran, R. Sabry, Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A, 299, (2002), 179-188.
  • H. Chen, H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos Soliton Fract, 19, (2004), 71-76.
  • Z. Fu, S. Liu, Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A, 290, (2001), 72-76.
  • S. Shen, Z. Pan, A note on the Jacobi elliptic function expansion method, Phys. Let. A, 308, (2003), 143-148.
  • H. T. Chen, Z. Hong-Qing, New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinesq equation, Chaos Soliton Fract, 20, (2004), 765-769.
  • Y. Chen, Q. Wang, B. Li, Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations, Z. Naturforsch. A, 59, (2004), 529-536.
  • Y. Chen, Z. Yan, The Weierstrass elliptic function expansion method and its appli-cations in nonlinear wave equations, Chaos Soliton Fract, 29, (2006), 948-964.
  • M. Wang, X. Li, J. Zhang, The -expansion method and travelling wave soluti-ons of nonlinear evolutions equations in mathematical physics, Phys. Lett. A, 372, (2008), 417-423.
  • S.Guo, Y. Zhou, The extended -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations, Appl. Math. Comput., 215, (2010), 3214-3221.
  • H. L. Lü, X. Q. Liu, L. Niu, A generalized expansion method and its applicati-ons to nonlinear evolution equations, Appl. Math. Comput., 215, (2010), 3811-3816.
  • L. Li, E. Li, M. Wang, The -expansion method and its application to travelling wave solutions of the Zakharov equations, Appl. Math-A J. Chin. U, 25, (2010), 454-462.
  • J. Manafian, Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan–expansion Method, Optik, 127, (2016), 4222-4245.
Yıl 2019, Cilt: 16 Sayı: 1, 54 - 62, 31.05.2019

Öz

Kaynakça

  • L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, MA, 1997.
  • A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam, 2002.
  • Y. Shang, Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation, Appl.Math.Comput. 187, (2007), 1286-1297.
  • T. L. Bock, M.D. Kruskal, A two-parameter Miura transformation of the Benjamin-Ono equation, Phys. Lett. A 74, (1979), 173-176.
  • V. B. Matveev, M.A. Salle, Darboux Transformations and Solitons, Springer, Berlin, 1991.
  • A. M. Abourabia, M. M. El Horbaty, On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation, Chaos Solitons Fractals, 29, (2006), 354-364.
  • Y. Chuntao, A simple transformation for nonlinear waves, Phys. Lett. A, 224, (1996), 77-84.
  • F. Cariello, M. Tabor, Painleve expansions for nonintegrable evolution equations, Physica D, 39, (1989), 77-94.
  • E. Fan, Two new application of the homogeneous balance method, Phys. Lett. A, 265, (2000), 353-357.
  • P. A. Clarkson, New similarity solutions for the modified boussinesq equation, J. Phys. A: Math. Gen., 22, (1989), 2355-2367.
  • W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, (1992), 650-654.
  • W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60, (1992), 650-654.
  • E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277, (2000), 212-218.
  • S. A. Elwakil, S.K. El-labany, M.A. Zahran, R. Sabry, Modified extended tanh-function method for solving nonlinear partial differential equations, Phys. Lett. A, 299, (2002), 179-188.
  • H. Chen, H. Zhang, New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation, Chaos Soliton Fract, 19, (2004), 71-76.
  • Z. Fu, S. Liu, Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A, 290, (2001), 72-76.
  • S. Shen, Z. Pan, A note on the Jacobi elliptic function expansion method, Phys. Let. A, 308, (2003), 143-148.
  • H. T. Chen, Z. Hong-Qing, New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinesq equation, Chaos Soliton Fract, 20, (2004), 765-769.
  • Y. Chen, Q. Wang, B. Li, Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations, Z. Naturforsch. A, 59, (2004), 529-536.
  • Y. Chen, Z. Yan, The Weierstrass elliptic function expansion method and its appli-cations in nonlinear wave equations, Chaos Soliton Fract, 29, (2006), 948-964.
  • M. Wang, X. Li, J. Zhang, The -expansion method and travelling wave soluti-ons of nonlinear evolutions equations in mathematical physics, Phys. Lett. A, 372, (2008), 417-423.
  • S.Guo, Y. Zhou, The extended -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations, Appl. Math. Comput., 215, (2010), 3214-3221.
  • H. L. Lü, X. Q. Liu, L. Niu, A generalized expansion method and its applicati-ons to nonlinear evolution equations, Appl. Math. Comput., 215, (2010), 3811-3816.
  • L. Li, E. Li, M. Wang, The -expansion method and its application to travelling wave solutions of the Zakharov equations, Appl. Math-A J. Chin. U, 25, (2010), 454-462.
  • J. Manafian, Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan–expansion Method, Optik, 127, (2016), 4222-4245.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

İbrahim Enam İNAN

Yayımlanma Tarihi 31 Mayıs 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 16 Sayı: 1

Kaynak Göster

APA İNAN, İ. E. (2019). Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation. Cankaya University Journal of Science and Engineering, 16(1), 54-62.
AMA İNAN İE. Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation. CUJSE. Mayıs 2019;16(1):54-62.
Chicago İNAN, İbrahim Enam. “Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation”. Cankaya University Journal of Science and Engineering 16, sy. 1 (Mayıs 2019): 54-62.
EndNote İNAN İE (01 Mayıs 2019) Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation. Cankaya University Journal of Science and Engineering 16 1 54–62.
IEEE İ. E. İNAN, “Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation”, CUJSE, c. 16, sy. 1, ss. 54–62, 2019.
ISNAD İNAN, İbrahim Enam. “Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation”. Cankaya University Journal of Science and Engineering 16/1 (Mayıs 2019), 54-62.
JAMA İNAN İE. Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation. CUJSE. 2019;16:54–62.
MLA İNAN, İbrahim Enam. “Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation”. Cankaya University Journal of Science and Engineering, c. 16, sy. 1, 2019, ss. 54-62.
Vancouver İNAN İE. Some Traveling Wave Solutions of (3+1)-Dimensional Jimbo-Miwa Equation. CUJSE. 2019;16(1):54-62.