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

Yavuz Uğurlu Doğan Kaya İbrahim E. İnan

https://izlik.org/JA55ZH43XC

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.

Keywords

SRLW equation , (1+1)-dimensional dispersive long wave equation , generalized Jacobi elliptic function method , periodic solutions , traveling wave solutions

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.