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Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method

Year 2009, Volume: 12 Issue: 2, 103 - 110, 01.04.2009

İbrahim E. İnan Yavuz Uğurlu Bülent Kılıç

Abstract

Bu çalışmada, RLW-Burgers ve potansiyel KdV denklemlerinin hareket eden dalga çözümleri içinaçılım metodu sunulur. Bu metot yardımı ile yukarıda bahsedilen denklemlerin bazı hareket eden dalga çözümleri bulunur

Keywords

RLW-Burgers denklemi Potansiyel KdV denklemi açılım metot Hareket eden dalga çözümler

References

  • M. Wang, X. Li, J. Zhang, ‘The (G'/G) expansion method and traveling wave solutions of nonlinear evolutions in mathematical physics’, Physics Letters A, 372 (2008), pp. 417-423.
  • H. Zhang, ‘New application of the (G'/G) expansion method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 3220-3225.
  • I. Aslan, T. Oziş, ‘Analytic study on two nonlinear evolution equations by using the (G'/G) expansion method’, Applied Mathematics and Computation, 209 (2009), pp. 425-429.
  • I. Aslan, T. Oziş, ‘On the validity and reliability of the (G'/G) expansion method by using higher-order nonlinear equations’, Applied Mathematics and Computation, 211 (2009), pp. 531-536.
  • A. Bekir, ‘Application of the (G'/G) expansion method for nonlinear evolution equations’, Physics Letters A, 372 (2008), pp. 3400-3406.
  • S. Zhang, W. Wang and J.L. Tong, ‘A generalized (G'/G) expansion method and its application to the (2+1) dimensional Broer-Kaup equations’, Applied Mathematics and Computation, 209 (2009), pp. 399-404.
  • S. Zhang, L.Dong, J- Mei. Ba, Y-Na Sun, ‘The (G'/G) expansion method for nonlinear differential difference equations’, Physics Letters A, 373 (2009), pp. 905-910.
  • 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).
  • M. A. Abdou, S. Zhang, ‘New periodic wave solutions via extended mapping method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 2-11.
  • M. A. Abdou, ‘New exact traveling wave solutions for the generalized nonlinear Schroedinger equation with a source’, Chaos Solitons Fractals, 38 (2008), pp. 949-955.
  • A. M. Wazwaz, ‘A study of nonlinear dispersive equations with solitary-wave solutions having compact support’, Mathematics and Computers in Simulation, 56 (2001), pp. 269-276.
  • Y. Lei, Z. Fajiang, W. Yinghai, ‘The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation’, Chaos Solitons Fractals, 13 (2002), pp. 337-340.
  • A. H. Khater, O.H. El-Kalaawy, M.A. Helal, ‘Two new classes of exact solutions for the KdV equation via Bäcklund transformations’, Chaos, Solitons & Fractals, 12 (1997), pp. 1901-1909.
  • M. L. Wang, ‘Exact solutions for a compound KdV-Burgers equation’, Physics Letters A, 213 (1996), pp. 279-287.
  • 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), pp. 67-75.
  • 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), pp. 599-609.
  • 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), pp. 1101-1112.
  • B. R. Duffy, E. J. Parkes, ‘Travelling solitary wave solutions to a seventh-order generalized KdV equation’, Physics Letters A, 214 (1996), pp. 271-272.
  • E. J. Parkes, B. R. Duffy, ‘Travelling solitary wave solutions to a compound KdV-Burgers equation’, Physics Letters A, 229 (1997), pp. 217-220.
  • 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), pp. 158-167.
  • 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), pp. 2962-2970.
  • 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), pp. 55-65.
  • D. S. Wang, H. Li, ‘Single and multi-solitary wave solutions to a class of nonlinear evolution equations’, Journal of Mathematical Analysis and Applications, 343 (2008), pp. 273-298.
  • T. Oziş, A. Yıldırım, ‘Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation’, Chaos,Solitons & Fractals, 38 (2008), pp. 209-212.
  • A.Yıldırım, ‘Application of He s homotopy perturbation method for solving the Cauchy reactiondiffusion problem’, Computers & Mathematics with Applications, 57 (2009), pp. 612-618.
  • A.Yıldırım, ‘Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations’, Communications in Numerical Methods in Engineering, (2008) (in press).
  • T.Oziş, A.Yıldırım, ‘Comparison between Adomian’s method and He’s homotopy perturbation method’, Computers & Mathematics with Applications, 56 (2008), pp. 1216-1224.
  • A.Yıldırım, ‘An Algorithm for Solving the Fractional Nonlinear Schrödinger Equation by Means of the Homotopy Perturbation Method’, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), pp. 445-451.
  • W. Hereman, A. Korpel and P.P. Banerjee, Wave Motion 7 (1985), pp. 283-289.
  • W. Hereman and 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), pp. 4805-4822.
  • H. Lan and K. Wang, ‘Exact solutions for two nonlinear equations’, Journal of Physics A: Mathematical and General 23 (1990), pp. 3923-3928.
  • S. Lou, G. Huang and H. Ruan, ‘Exact solitary waves in a convecting fluid’, Journal of Physics A: Mathematical and General 24 (1991), pp. L587-L590.
  • W. Malfliet, ‘Solitary wave solutions of nonlinear wave equations’, American Journal of Physics 60 (1992), pp. 650-654.
  • E. J. Parkes and B. R. Duffy, ‘An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations’, Computer Physics Communications 98 (1996), pp. 288-300.
  • E. Fan, ‘Extended tanh-function method and its applications to nonlinear equations’, Physics Letters A 277 (2000), pp. 212-218.
  • 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), pp. 179-188.
  • 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), pp. 145-157.
  • E. Yomba, ‘Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation’, Chaos, Solitons & Fractals, 20 (2004), pp. 1135-1139.
  • H. Chen and H. Zhang, ‘New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation’, Chaos, Solitons & Fractals, 19 (2004), pp. 71-76.

Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method

Year 2009, Volume: 12 Issue: 2, 103 - 110, 01.04.2009

İbrahim E. İnan Yavuz Uğurlu Bülent Kılıç

Abstract



Keywords

-

References

  • M. Wang, X. Li, J. Zhang, ‘The (G'/G) expansion method and traveling wave solutions of nonlinear evolutions in mathematical physics’, Physics Letters A, 372 (2008), pp. 417-423.
  • H. Zhang, ‘New application of the (G'/G) expansion method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 3220-3225.
  • I. Aslan, T. Oziş, ‘Analytic study on two nonlinear evolution equations by using the (G'/G) expansion method’, Applied Mathematics and Computation, 209 (2009), pp. 425-429.
  • I. Aslan, T. Oziş, ‘On the validity and reliability of the (G'/G) expansion method by using higher-order nonlinear equations’, Applied Mathematics and Computation, 211 (2009), pp. 531-536.
  • A. Bekir, ‘Application of the (G'/G) expansion method for nonlinear evolution equations’, Physics Letters A, 372 (2008), pp. 3400-3406.
  • S. Zhang, W. Wang and J.L. Tong, ‘A generalized (G'/G) expansion method and its application to the (2+1) dimensional Broer-Kaup equations’, Applied Mathematics and Computation, 209 (2009), pp. 399-404.
  • S. Zhang, L.Dong, J- Mei. Ba, Y-Na Sun, ‘The (G'/G) expansion method for nonlinear differential difference equations’, Physics Letters A, 373 (2009), pp. 905-910.
  • 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).
  • M. A. Abdou, S. Zhang, ‘New periodic wave solutions via extended mapping method’, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 2-11.
  • M. A. Abdou, ‘New exact traveling wave solutions for the generalized nonlinear Schroedinger equation with a source’, Chaos Solitons Fractals, 38 (2008), pp. 949-955.
  • A. M. Wazwaz, ‘A study of nonlinear dispersive equations with solitary-wave solutions having compact support’, Mathematics and Computers in Simulation, 56 (2001), pp. 269-276.
  • Y. Lei, Z. Fajiang, W. Yinghai, ‘The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation’, Chaos Solitons Fractals, 13 (2002), pp. 337-340.
  • A. H. Khater, O.H. El-Kalaawy, M.A. Helal, ‘Two new classes of exact solutions for the KdV equation via Bäcklund transformations’, Chaos, Solitons & Fractals, 12 (1997), pp. 1901-1909.
  • M. L. Wang, ‘Exact solutions for a compound KdV-Burgers equation’, Physics Letters A, 213 (1996), pp. 279-287.
  • 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), pp. 67-75.
  • 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), pp. 599-609.
  • 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), pp. 1101-1112.
  • B. R. Duffy, E. J. Parkes, ‘Travelling solitary wave solutions to a seventh-order generalized KdV equation’, Physics Letters A, 214 (1996), pp. 271-272.
  • E. J. Parkes, B. R. Duffy, ‘Travelling solitary wave solutions to a compound KdV-Burgers equation’, Physics Letters A, 229 (1997), pp. 217-220.
  • 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), pp. 158-167.
  • 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), pp. 2962-2970.
  • 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), pp. 55-65.
  • D. S. Wang, H. Li, ‘Single and multi-solitary wave solutions to a class of nonlinear evolution equations’, Journal of Mathematical Analysis and Applications, 343 (2008), pp. 273-298.
  • T. Oziş, A. Yıldırım, ‘Reliable analysis for obtaining exact soliton solutions of nonlinear Schrödinger (NLS) equation’, Chaos,Solitons & Fractals, 38 (2008), pp. 209-212.
  • A.Yıldırım, ‘Application of He s homotopy perturbation method for solving the Cauchy reactiondiffusion problem’, Computers & Mathematics with Applications, 57 (2009), pp. 612-618.
  • A.Yıldırım, ‘Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations’, Communications in Numerical Methods in Engineering, (2008) (in press).
  • T.Oziş, A.Yıldırım, ‘Comparison between Adomian’s method and He’s homotopy perturbation method’, Computers & Mathematics with Applications, 56 (2008), pp. 1216-1224.
  • A.Yıldırım, ‘An Algorithm for Solving the Fractional Nonlinear Schrödinger Equation by Means of the Homotopy Perturbation Method’, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), pp. 445-451.
  • W. Hereman, A. Korpel and P.P. Banerjee, Wave Motion 7 (1985), pp. 283-289.
  • W. Hereman and 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), pp. 4805-4822.
  • H. Lan and K. Wang, ‘Exact solutions for two nonlinear equations’, Journal of Physics A: Mathematical and General 23 (1990), pp. 3923-3928.
  • S. Lou, G. Huang and H. Ruan, ‘Exact solitary waves in a convecting fluid’, Journal of Physics A: Mathematical and General 24 (1991), pp. L587-L590.
  • W. Malfliet, ‘Solitary wave solutions of nonlinear wave equations’, American Journal of Physics 60 (1992), pp. 650-654.
  • E. J. Parkes and B. R. Duffy, ‘An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations’, Computer Physics Communications 98 (1996), pp. 288-300.
  • E. Fan, ‘Extended tanh-function method and its applications to nonlinear equations’, Physics Letters A 277 (2000), pp. 212-218.
  • 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), pp. 179-188.
  • 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), pp. 145-157.
  • E. Yomba, ‘Construction of new soliton-like solutions of the (2+1) dimensional dispersive long wave equation’, Chaos, Solitons & Fractals, 20 (2004), pp. 1135-1139.
  • H. Chen and H. Zhang, ‘New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation’, Chaos, Solitons & Fractals, 19 (2004), pp. 71-76.
There are 40 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

İbrahim E. İnan This is me

Yavuz Uğurlu This is me

Bülent Kılıç This is me

Publication Date April 1, 2009
Published in Issue Year 2009 Volume: 12 Issue: 2

Cite

APA İnan, İ. E., Uğurlu, Y., & Kılıç, B. (2009). Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method. Cankaya University Journal of Science and Engineering, 12(2), 103-110.
AMA İnan İE, Uğurlu Y, Kılıç B. Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method. CUJSE. April 2009;12(2):103-110.
Chicago İnan, İbrahim E., Yavuz Uğurlu, and Bülent Kılıç. “Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method”. Cankaya University Journal of Science and Engineering 12, no. 2 (April 2009): 103-10.
EndNote İnan İE, Uğurlu Y, Kılıç B (April 1, 2009) Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method. Cankaya University Journal of Science and Engineering 12 2 103–110.
IEEE İ. E. İnan, Y. Uğurlu, and B. Kılıç, “Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method”, CUJSE, vol. 12, no. 2, pp. 103–110, 2009.
ISNAD İnan, İbrahim E. et al. “Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method”. Cankaya University Journal of Science and Engineering 12/2 (April 2009), 103-110.
JAMA İnan İE, Uğurlu Y, Kılıç B. Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method. CUJSE. 2009;12:103–110.
MLA İnan, İbrahim E. et al. “Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method”. Cankaya University Journal of Science and Engineering, vol. 12, no. 2, 2009, pp. 103-10.
Vancouver İnan İE, Uğurlu Y, Kılıç B. Traveling Wave Solutions of the RLW-Burgers Equation and Potential Kdv Equation by Using the - Expansion Method. CUJSE. 2009;12(2):103-10.