Yıl 2011,
Cilt: 8 Sayı: 2, - , 01.11.2011
Yavuz Uğurlu
Doğan Kaya
İbrahim E. İnan
Kaynakça
- [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
Yıl 2011,
Cilt: 8 Sayı: 2, - , 01.11.2011
Yavuz Uğurlu
Doğan Kaya
İbrahim E. İnan
Öz
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.
Kaynakça
- [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.