Araştırma Makalesi
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Yıl 2019, Cilt 1, Sayı 2, 100 - 109, 30.08.2019

Öz

Kaynakça

  • [1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers. Boston: MA- Birkhauser. 1997.
  • [2] A.M. Wazwaz, Partial Differential Equations: Methods and Applications. Rotterdam: Balkema. 2002.
  • [3] Y. Shang, “Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation”, Applied Math.Comput., 187, 1286-1297, 2007.
  • [4] T.L. Bock, M.D. Kruskal, “A two-parameter Miura transformation of the Benjamin-Ono equation”, Physics Letters A, 74 , 173-176, 1979.
  • [5] V.B. Matveev, M.A. Salle, Darboux Transformations and Solitons, Berlin: Springer , 1991.
  • [6] A.M. Abourabia, M.M. El Horbaty, “On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation”, Chaos Solitons and Fractals, 29, 354-364, 2006.
  • [7] W. Malfliet, “Solitary wave solutions of nonlinear wave equations”, American Journal of Physics, 60, 650-654, 1992.
  • [8] Y. Chuntao, “A simple transformation for nonlinear waves”, Physics Letters A, 224, 77-84, 1996.
  • [9] F. Cariello, M. Tabor, “Painleve expansions for nonintegrable evolution equations”, Physica D, 39, 77-94, 1989.
  • [10] E. Fan, “Two new application of the homogeneous balance method”, Physics Letters A, 265, 353-357, 2000.
  • [11] P.A. Clarkson, “New similarity solutions for the modified boussinesq equation”, Journal of Physics A: Mathematical and General, 22, 2355-2367, 1989.
  • [12] E. Fan,” Extended tanh-function method and its applications to nonlinear equations”, Physics Letters A, 277, 212-218, 2000.
  • [13] S. A. Elwakil, S.K. El-labany, M.A. Zahran, R. Sabry, “Modified extended tanh-function method for solving nonlinear partial differential equations”, Physics Letters A, 299, 179-188, 2002.
  • [14] H. Chen, H. Zhang, “New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation”, Chaos Solitons and Fractals, 19, 71-76, 2004.
  • [15] Z. Fu, S. Liu, Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations”, Physics Letters A, 290, 72-76, 2001.
  • [16] S. Shen, Z. Pan, “A note on the Jacobi elliptic function expansion method”, Physics Letters A, 308, 143-148, 2003.
  • [17] H. T. Chen, Z. Hong-Qing, “New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinesq equation”, Chaos Solitons and Fractals, 20, 765-769, 2004.
  • [18] 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”, Zeitschrift für Naturforschung A, 59, 529-536, 2004.
  • [19] Y. Chen, Z. Yan, “The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations”, Chaos Solitons and Fractals, 29, 948-964, 2006.
  • [20] M. Wang, X. Li, J. Zhang, “The -expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics”, Physics Letters A, 372, 417-423, 2008.
  • [21] S.Guo, Y. Zhou, “The extended -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations”, Applied Mathematics and Computation, 215, 3214-3221, 2010.
  • [22] H. L. Lü, X. Q. Liu, L. Niu, “A generalized -expansion method and its applications to nonlinear evolution equations”, Applied Mathematics and Computation, 215, 3811-3816, 2010.
  • [23] L. Li, E. Li, M. Wang, “The -expansion method and its application to travelling wave solutions of the Zakharov equations”, Applied Mathematics-A Journal of Chinese Universities, 25, 454-462, 2010.
  • [24] J. Manafian, “Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan – expansion Method”, Optik, 127, 4222-4245, 2016.
  • [25] Mostafa M.A Khater, “Extended Exp(−𝜑(ξ))-Expansion Method for Solving the Generalized Hirota-Satsuma Coupled KdV System”, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15, 7, Version 1.0 Year 2015.
  • [26] Mostafa M.A Khater and Emad H.M. Zahran, “Modified extended tanh function method and its applications to the Bogoyavlenskii equation”, Applied Mathematical Modelling,40, 1769-1775, 2016.
  • [27] Mostafa M.A Khater, Emad H.M. Zahran, “Soliton Soltuions of Nonlinear Evolutions Equation by using the Extended Exp (-φ (ξ)) Expansion Method”, International Journal of Computer Applications, 145, 1-5, 2016.
  • [28] Q. Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, “Optical solitons with Biswas–Milovic equation by extended (G /G)-expansion method”, Optik, 127, 16, 6277–6290, 2016.
  • [29] J.Manafian, M.F. Aghdaei, M.Khalilian and R.S.Jeddi, “Application of the generalized -expansion method for nonlinear PDEs to obtaining soliton wave solution”, Optik, 135, 395–406, 2017.
  • [30] G. Ebadi, A. Biswas, “Application of the G /G-expansion method for nonlinear diffusion equations with nonlinear source”, Journal of the Franklin Institute, 347, 7, 1391–1398, 2010.
  • [31] M. Mirzazadeh, M. Eslami, A. Biswas, “1-Soliton solution of KdV6 equation”, Nonlinear Dynamics, 80, 1–2, 387–396, 2015.
  • [32] Zheyna Yan, “New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations”, Physics Letters A, 292, 100-106, 2001.
  • [33] M.M.A. Khater, A.R. Seadawy and d. Lu, “Dispersive solitary wave solutions of new coupled Konno-Oono, Higgs field and Maccari equations and their applications”, Journal of King Saud University, 30, 417–423, 2018.
  • [34] X. Zhao, L. Wang, W. Sun, “The repeated homogeneous balance method and its applications to nonlinear partial differential equations”, Chaos Solitons and Fractals, 28, 448–453, 2006.
  • [35] A. Biswas, E. Topkara, S. Johnson, E. Zerrad, S. Konar, “Quasi-stationary optical solitons in non-Kerr law media with full nonlinearity”, Journal of Nonlinear Optical Physics & Materials, 20, 309–325, 2011.
  • [36] A. Biswas, A.B. Aceves,” Dynamics of solitons in optical fibers”, Journal of Modern Optics, 48, 1135–1150, 2001.
  • [37] Feng Q, Zheng B.,” Traveling wave solutions for the fifth-order Sawada-Kotera equation and the general Gardner equation by (G’/G)-expansion method”, Wseas Transactions on Mathematics, 9(3), 171–80, 2010.
  • [38] A.M. Wazwaz, “Burgers hierarchy: Multiple kink solutions and multiple singular kink solutions”, Journal of the Franklin Institute, 347, 618–626, 2010.
  • [39] E.M.E. Zayed, M.A.M. Abdelaziz, “The two variables (G’/G, 1/G) -expansion method for solving the nonlinear KdV-mKdV equation”, Mathematical Problems in Engineering, article ID 725061, 14 pp, 2012.
  • [40] E.M.E. Zayed, S.A. Hoda Ibrahim, M.A.M. Abdelaziz, “Traveling wave solutions of the nonlinear (3+1) dimensional Kadomtsev–Petviashvili equation using the two variables ( G’/G , 1/G) -expansion method”, Journal Applied Mathematics, article ID 560531, 8 pp, 2012.
  • [41] S. El-Ganaini, M. Mirzazadeh, A. Biswas, “Solitons and other solutions to long-short wave resonance equation, Applied Mathematics and Computation, 14 (3), 248–259, 2015.
  • [42] Mostafa M.A Khater and Emad H.M. Zahran,” New solitary wave solution of the generalized Hirota-Satsuma couple KdV system”, International Journal of Scientific &Engineering Research, 6, 1324-1331, 2015.
  • [43] J. Manafian Heris, M. Lakestani, “Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n, n)-Burger equations by the generalized tanh-coth method”, Communications in Numerical Analysis, 1–18, 2013.
  • [44] A.M.Wazwaz, H. Triki,” Multiple soliton solutions for the sixth-order Ramani equation and a coupled Ramani equation”, Applied Mathematics and Computation, 216, 332–336, 2010.
  • [45] A.M. Wazwaz, “The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations”, Applied Mathematics and Computation, 188 (2), 1467–1475, 2007.
  • [46] J. Manafian Heris, I. Zamanpour,” Analytical treatment of the coupled Higgs equation and the Maccari system via Exp-function method”, Acta Universitatis Apulensis, 33, 203–216, 2013.
  • [47] C. Kong , D. Wang, L. Song, H. Zhang, “New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method”, Chaos, Solitons and Fractals, 39, 697–706 2009.

Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)

Yıl 2019, Cilt 1, Sayı 2, 100 - 109, 30.08.2019

Öz

In this article, we have found some soliton wave solutions of the (2 + 1) -dimensional dispersive long wave equation using the generalized  - expansion method. For this equation, we obtained hyperbolic function solutions, exponential function solutions and rational function solutions. We also saw that the solutions provided the equation using Mathematica 11.2 and we showed the graphical performance of some of the solutions found.

Kaynakça

  • [1] L. Debtnath, Nonlinear Partial Differential Equations for Scientist and Engineers. Boston: MA- Birkhauser. 1997.
  • [2] A.M. Wazwaz, Partial Differential Equations: Methods and Applications. Rotterdam: Balkema. 2002.
  • [3] Y. Shang, “Backlund transformation, Lax pairs and explicit exact solutions for the shallow water waves equation”, Applied Math.Comput., 187, 1286-1297, 2007.
  • [4] T.L. Bock, M.D. Kruskal, “A two-parameter Miura transformation of the Benjamin-Ono equation”, Physics Letters A, 74 , 173-176, 1979.
  • [5] V.B. Matveev, M.A. Salle, Darboux Transformations and Solitons, Berlin: Springer , 1991.
  • [6] A.M. Abourabia, M.M. El Horbaty, “On solitary wave solutions for the two-dimensional nonlinear modified Kortweg-de Vries-Burger equation”, Chaos Solitons and Fractals, 29, 354-364, 2006.
  • [7] W. Malfliet, “Solitary wave solutions of nonlinear wave equations”, American Journal of Physics, 60, 650-654, 1992.
  • [8] Y. Chuntao, “A simple transformation for nonlinear waves”, Physics Letters A, 224, 77-84, 1996.
  • [9] F. Cariello, M. Tabor, “Painleve expansions for nonintegrable evolution equations”, Physica D, 39, 77-94, 1989.
  • [10] E. Fan, “Two new application of the homogeneous balance method”, Physics Letters A, 265, 353-357, 2000.
  • [11] P.A. Clarkson, “New similarity solutions for the modified boussinesq equation”, Journal of Physics A: Mathematical and General, 22, 2355-2367, 1989.
  • [12] E. Fan,” Extended tanh-function method and its applications to nonlinear equations”, Physics Letters A, 277, 212-218, 2000.
  • [13] S. A. Elwakil, S.K. El-labany, M.A. Zahran, R. Sabry, “Modified extended tanh-function method for solving nonlinear partial differential equations”, Physics Letters A, 299, 179-188, 2002.
  • [14] H. Chen, H. Zhang, “New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation”, Chaos Solitons and Fractals, 19, 71-76, 2004.
  • [15] Z. Fu, S. Liu, Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations”, Physics Letters A, 290, 72-76, 2001.
  • [16] S. Shen, Z. Pan, “A note on the Jacobi elliptic function expansion method”, Physics Letters A, 308, 143-148, 2003.
  • [17] H. T. Chen, Z. Hong-Qing, “New double periodic and multiple soliton solutions of the generalized (2+1)-dimensional Boussinesq equation”, Chaos Solitons and Fractals, 20, 765-769, 2004.
  • [18] 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”, Zeitschrift für Naturforschung A, 59, 529-536, 2004.
  • [19] Y. Chen, Z. Yan, “The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations”, Chaos Solitons and Fractals, 29, 948-964, 2006.
  • [20] M. Wang, X. Li, J. Zhang, “The -expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics”, Physics Letters A, 372, 417-423, 2008.
  • [21] S.Guo, Y. Zhou, “The extended -expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations”, Applied Mathematics and Computation, 215, 3214-3221, 2010.
  • [22] H. L. Lü, X. Q. Liu, L. Niu, “A generalized -expansion method and its applications to nonlinear evolution equations”, Applied Mathematics and Computation, 215, 3811-3816, 2010.
  • [23] L. Li, E. Li, M. Wang, “The -expansion method and its application to travelling wave solutions of the Zakharov equations”, Applied Mathematics-A Journal of Chinese Universities, 25, 454-462, 2010.
  • [24] J. Manafian, “Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan – expansion Method”, Optik, 127, 4222-4245, 2016.
  • [25] Mostafa M.A Khater, “Extended Exp(−𝜑(ξ))-Expansion Method for Solving the Generalized Hirota-Satsuma Coupled KdV System”, Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15, 7, Version 1.0 Year 2015.
  • [26] Mostafa M.A Khater and Emad H.M. Zahran, “Modified extended tanh function method and its applications to the Bogoyavlenskii equation”, Applied Mathematical Modelling,40, 1769-1775, 2016.
  • [27] Mostafa M.A Khater, Emad H.M. Zahran, “Soliton Soltuions of Nonlinear Evolutions Equation by using the Extended Exp (-φ (ξ)) Expansion Method”, International Journal of Computer Applications, 145, 1-5, 2016.
  • [28] Q. Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, “Optical solitons with Biswas–Milovic equation by extended (G /G)-expansion method”, Optik, 127, 16, 6277–6290, 2016.
  • [29] J.Manafian, M.F. Aghdaei, M.Khalilian and R.S.Jeddi, “Application of the generalized -expansion method for nonlinear PDEs to obtaining soliton wave solution”, Optik, 135, 395–406, 2017.
  • [30] G. Ebadi, A. Biswas, “Application of the G /G-expansion method for nonlinear diffusion equations with nonlinear source”, Journal of the Franklin Institute, 347, 7, 1391–1398, 2010.
  • [31] M. Mirzazadeh, M. Eslami, A. Biswas, “1-Soliton solution of KdV6 equation”, Nonlinear Dynamics, 80, 1–2, 387–396, 2015.
  • [32] Zheyna Yan, “New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations”, Physics Letters A, 292, 100-106, 2001.
  • [33] M.M.A. Khater, A.R. Seadawy and d. Lu, “Dispersive solitary wave solutions of new coupled Konno-Oono, Higgs field and Maccari equations and their applications”, Journal of King Saud University, 30, 417–423, 2018.
  • [34] X. Zhao, L. Wang, W. Sun, “The repeated homogeneous balance method and its applications to nonlinear partial differential equations”, Chaos Solitons and Fractals, 28, 448–453, 2006.
  • [35] A. Biswas, E. Topkara, S. Johnson, E. Zerrad, S. Konar, “Quasi-stationary optical solitons in non-Kerr law media with full nonlinearity”, Journal of Nonlinear Optical Physics & Materials, 20, 309–325, 2011.
  • [36] A. Biswas, A.B. Aceves,” Dynamics of solitons in optical fibers”, Journal of Modern Optics, 48, 1135–1150, 2001.
  • [37] Feng Q, Zheng B.,” Traveling wave solutions for the fifth-order Sawada-Kotera equation and the general Gardner equation by (G’/G)-expansion method”, Wseas Transactions on Mathematics, 9(3), 171–80, 2010.
  • [38] A.M. Wazwaz, “Burgers hierarchy: Multiple kink solutions and multiple singular kink solutions”, Journal of the Franklin Institute, 347, 618–626, 2010.
  • [39] E.M.E. Zayed, M.A.M. Abdelaziz, “The two variables (G’/G, 1/G) -expansion method for solving the nonlinear KdV-mKdV equation”, Mathematical Problems in Engineering, article ID 725061, 14 pp, 2012.
  • [40] E.M.E. Zayed, S.A. Hoda Ibrahim, M.A.M. Abdelaziz, “Traveling wave solutions of the nonlinear (3+1) dimensional Kadomtsev–Petviashvili equation using the two variables ( G’/G , 1/G) -expansion method”, Journal Applied Mathematics, article ID 560531, 8 pp, 2012.
  • [41] S. El-Ganaini, M. Mirzazadeh, A. Biswas, “Solitons and other solutions to long-short wave resonance equation, Applied Mathematics and Computation, 14 (3), 248–259, 2015.
  • [42] Mostafa M.A Khater and Emad H.M. Zahran,” New solitary wave solution of the generalized Hirota-Satsuma couple KdV system”, International Journal of Scientific &Engineering Research, 6, 1324-1331, 2015.
  • [43] J. Manafian Heris, M. Lakestani, “Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n, n)-Burger equations by the generalized tanh-coth method”, Communications in Numerical Analysis, 1–18, 2013.
  • [44] A.M.Wazwaz, H. Triki,” Multiple soliton solutions for the sixth-order Ramani equation and a coupled Ramani equation”, Applied Mathematics and Computation, 216, 332–336, 2010.
  • [45] A.M. Wazwaz, “The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations”, Applied Mathematics and Computation, 188 (2), 1467–1475, 2007.
  • [46] J. Manafian Heris, I. Zamanpour,” Analytical treatment of the coupled Higgs equation and the Maccari system via Exp-function method”, Acta Universitatis Apulensis, 33, 203–216, 2013.
  • [47] C. Kong , D. Wang, L. Song, H. Zhang, “New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method”, Chaos, Solitons and Fractals, 39, 697–706 2009.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

İbrahim Enam İNAN> (Sorumlu Yazar)

0000-0002-2415-0471
Türkiye

Yayımlanma Tarihi 30 Ağustos 2019
Gönderilme Tarihi 26 Mart 2019
Kabul Tarihi 26 Ağustos 2019
Yayınlandığı Sayı Yıl 2019, Cilt 1, Sayı 2

Kaynak Göster

Bibtex @araştırma makalesi { alku544651, journal = {ALKÜ Fen Bilimleri Dergisi}, eissn = {2667-7814}, address = {}, publisher = {Alanya Alaaddin Keykubat Üniversitesi}, year = {2019}, volume = {1}, number = {2}, pages = {100 - 109}, title = {Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)}, key = {cite}, author = {İnan, İbrahim Enam} }
APA İnan, İ. E. (2019). Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE) . ALKÜ Fen Bilimleri Dergisi , 1 (2) , 100-109 . Retrieved from https://dergipark.org.tr/tr/pub/alku/issue/42573/544651
MLA İnan, İ. E. "Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)" . ALKÜ Fen Bilimleri Dergisi 1 (2019 ): 100-109 <https://dergipark.org.tr/tr/pub/alku/issue/42573/544651>
Chicago İnan, İ. E. "Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)". ALKÜ Fen Bilimleri Dergisi 1 (2019 ): 100-109
RIS TY - JOUR T1 - Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE) AU - İbrahim Enamİnan Y1 - 2019 PY - 2019 N1 - DO - T2 - ALKÜ Fen Bilimleri Dergisi JF - Journal JO - JOR SP - 100 EP - 109 VL - 1 IS - 2 SN - -2667-7814 M3 - UR - Y2 - 2019 ER -
EndNote %0 ALKÜ Fen Bilimleri Dergisi Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE) %A İbrahim Enam İnan %T Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE) %D 2019 %J ALKÜ Fen Bilimleri Dergisi %P -2667-7814 %V 1 %N 2 %R %U
ISNAD İnan, İbrahim Enam . "Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)". ALKÜ Fen Bilimleri Dergisi 1 / 2 (Ağustos 2019): 100-109 .
AMA İnan İ. E. Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE). ALKÜ Fen Bilimleri Dergisi. 2019; 1(2): 100-109.
Vancouver İnan İ. E. Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE). ALKÜ Fen Bilimleri Dergisi. 2019; 1(2): 100-109.
IEEE İ. E. İnan , "Generalized (G'/G) - Expansion Method for Some Soliton Wave Solution of (2+1)-Dimensional Dispersive Long Wave Equation (DLWE)", ALKÜ Fen Bilimleri Dergisi, c. 1, sayı. 2, ss. 100-109, Ağu. 2019