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Year 2011, Volume: 8 Issue: 2, - , 01.11.2011

Abstract

References

  • [1] 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), 288–300.
  • [2] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Physics Letters A 277 (2000), 212–218.
  • [3] 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.
  • [4] 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.
  • [5] Z. Fu, S. Liu, S. Liu and Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Physics Letters A 290 (2001), 72–76.
  • [6] Y. Chen, Q. Wang and B. Li, Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations, Zeitschrift fur Naturforschung A 59 (2004), 529–536.
  • [7] Y. Chen and Z. Yan, The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations, Chaos, Solitons & Fractals 29 (2006), 948–964.
  • [8] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals 30 (2006), 700–708.
  • [9] M. Wang, X. Li and J. Zhang, The (G0/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A 372 (2008), 417–423.
  • [10] H. L. Lu, X. Q. Liu and L. Niu, A generalized (G0/G)-expansion method and its applications to nonlinear evolution equations, Applied Mathematics and Computation 215 (2010), 3811-3816.
  • [11] H. T. Chen and 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.
  • [12] Y. Shang and B. Guo, Analysis of Chebyshev pseudospectral method for multi-dimensional generalized SRLW equations, Applied Mathematics and Mechanics 24 (2003), 1168–1183.
  • [13] S. Guo and Y. Zhou, The extended (G0/G)-expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations, Applied Mathematics and Computation 215 (2010), 3214–3221.
  • [14] L. Iskandar and P. C. Jain, Numerical solutions of the improved Boussinesq equation, Proceedings of the Indian Academy of Sciences 89 (1980), 171–181.
  • [15] M. P. Soerensen, P. L. Christainsen and P. S. Lomdahl, Solitary waves on nonlinear elastic rods, Journal of the Acoustical Society of America 76 (1984), 871–879.
  • [16] J. L. Bogolubsky, Some examples of inelastic soliton interaction, Computer Physics Communications 13 (1977), 149–155.
  • [17] F. Xu, Application of exp-function method to symmetric regularized long wave (SRLW) equation, Physics Letters A 372 (2008), 252–257.
  • [18] A. Bekir and A. C. Cevikel, New exact travelling wave solutions of nonlinear physical models, Chaos, Solitons & Fractals 41 (2009), 1733-1739.

Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation

Year 2011, Volume: 8 Issue: 2, - , 01.11.2011

Abstract

We implement the generalized Jacobi elliptic function method with symbolic
computation to construct periodic solutions for the symmetric regularized long wave
(SRLW) equation and (1+1)-dimensional dispersive long wave equation.

References

  • [1] 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), 288–300.
  • [2] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Physics Letters A 277 (2000), 212–218.
  • [3] 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.
  • [4] 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.
  • [5] Z. Fu, S. Liu, S. Liu and Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Physics Letters A 290 (2001), 72–76.
  • [6] Y. Chen, Q. Wang and B. Li, Jacobi elliptic function rational expansion method with symbolic computation to construct new doubly periodic solutions of nonlinear evolution equations, Zeitschrift fur Naturforschung A 59 (2004), 529–536.
  • [7] Y. Chen and Z. Yan, The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations, Chaos, Solitons & Fractals 29 (2006), 948–964.
  • [8] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals 30 (2006), 700–708.
  • [9] M. Wang, X. Li and J. Zhang, The (G0/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A 372 (2008), 417–423.
  • [10] H. L. Lu, X. Q. Liu and L. Niu, A generalized (G0/G)-expansion method and its applications to nonlinear evolution equations, Applied Mathematics and Computation 215 (2010), 3811-3816.
  • [11] H. T. Chen and 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.
  • [12] Y. Shang and B. Guo, Analysis of Chebyshev pseudospectral method for multi-dimensional generalized SRLW equations, Applied Mathematics and Mechanics 24 (2003), 1168–1183.
  • [13] S. Guo and Y. Zhou, The extended (G0/G)-expansion method and its applications to the Whitham-Broer-Kaup-Like equations and coupled Hirota-Satsuma KdV equations, Applied Mathematics and Computation 215 (2010), 3214–3221.
  • [14] L. Iskandar and P. C. Jain, Numerical solutions of the improved Boussinesq equation, Proceedings of the Indian Academy of Sciences 89 (1980), 171–181.
  • [15] M. P. Soerensen, P. L. Christainsen and P. S. Lomdahl, Solitary waves on nonlinear elastic rods, Journal of the Acoustical Society of America 76 (1984), 871–879.
  • [16] J. L. Bogolubsky, Some examples of inelastic soliton interaction, Computer Physics Communications 13 (1977), 149–155.
  • [17] F. Xu, Application of exp-function method to symmetric regularized long wave (SRLW) equation, Physics Letters A 372 (2008), 252–257.
  • [18] A. Bekir and A. C. Cevikel, New exact travelling wave solutions of nonlinear physical models, Chaos, Solitons & Fractals 41 (2009), 1733-1739.
There are 18 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Yavuz Uğurlu This is me

Doğan Kaya This is me

İbrahim E. İnan This is me

Publication Date November 1, 2011
Published in Issue Year 2011 Volume: 8 Issue: 2

Cite

APA Uğurlu, Y., Kaya, D., & İnan, İ. E. (2011). Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation. Cankaya University Journal of Science and Engineering, 8(2).
AMA Uğurlu Y, Kaya D, İnan İE. Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation. CUJSE. November 2011;8(2).
Chicago Uğurlu, Yavuz, Doğan Kaya, and İbrahim E. İnan. “Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation”. Cankaya University Journal of Science and Engineering 8, no. 2 (November 2011).
EndNote Uğurlu Y, Kaya D, İnan İE (November 1, 2011) Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation. Cankaya University Journal of Science and Engineering 8 2
IEEE Y. Uğurlu, D. Kaya, and İ. E. İnan, “Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation”, CUJSE, vol. 8, no. 2, 2011.
ISNAD Uğurlu, Yavuz et al. “Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation”. Cankaya University Journal of Science and Engineering 8/2 (November 2011).
JAMA Uğurlu Y, Kaya D, İnan İE. Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation. CUJSE. 2011;8.
MLA Uğurlu, Yavuz et al. “Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation”. Cankaya University Journal of Science and Engineering, vol. 8, no. 2, 2011.
Vancouver Uğurlu Y, Kaya D, İnan İE. Generalized Jacobi Elliptic Function Method for Periodic Wave Solutions of SRLW Equation and (1+1)-Dimensional Dispersive Long Wave Equation. CUJSE. 2011;8(2).