NEW APPROACH TO THE SOLUTIONS OF THE PIB EQUATION

Year 2011, Volume: 01 Issue: 1, 35 - 40, 01.06.2011

Jalil Rashidinia Ali Barati

Abstract

In this paper, based on the Exp-function method and mathematical derivation, we obtain several explicit and exact traveling wave solutions for the PIB equation.

Keywords

The Exp-function method , PIB equation , Traveling wave solution

References

• Ablowitz, M.J. and Segur, H., (1981), Soliton and the inverse scattering transformation, SIAM, Philadelphia, PA.
• He, J.H., (1999), Variational iteration method-a kind of non-linear analytical technique: some examples. Int. J. Non-linear Mech. 34 (4), 699-708.
• He, J.H., (2006), New interpretation of homotopy perturbation method. Int. J. Mod. Phys. B 20 (18), 2561-2568.
• He, J.H., (2005), Application of homotopy perturbation method to nonlinear wave equations, Chaos, Solitons and Fractals 26(3), 695-700.
• He, J.H., (2005), Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlin- ear Sci. Numer. Simul. 6 (2), 207-208.
• Wadati, M., (1975), Wave propagation in nonlinear lattice, I, J. Phys. Soc. Jpn. 38, 673-680.
• Wang, D.S. and Zhang, H.Q., (2005), Auto-Backlund transformation and new exact solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation, Int. J. Mod. Phys. C 16(3), 393.
• Wazwaz, A.M., (2005), The tanh method: solitons and periodic solutions for the Dodd-Bullough- Tzikhailov and the Tzitzeica-Dodd-Bullough equations, Chaos, Solitons and Fractals 25, 55-63.
• Franz, P. and Hongyou, W., (1995), Discretizing constant curvature surfaces via loop group factoriza- tions: the discrete sine- and sinh-Gordon equations, J. Geomet. Phys. 17 (3), 245-260.
• Xiqiang, Z., Limin, W. and Weijun, S., (2006), The repeated homogeneous balance method and its applications to nonlinear partial differential equations, Chaos, Solitons and Fractals 28(2), 448-453.
• Fan, E. and Jian, Z., (2002), Applications of the Jacobi elliptic function method to special-type nonlinear equations, Phys. Lett. A 305 (6), 383-392.
• Novikov, D.P., (1999), Algebraic geometric solutions of the Harry Dym equations, Math. J. 40, 136.
• He, J.H., (2006), Some asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B 20 (10), 1141-1199.
• He, J.H., (2006), X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals 30 (3), 700-708.
• He, J.H., (2006), Non-perturbative method for strongly nonlinear problems. Berlin: dissertation. De- Verlag im internet GmbH.
• El-Wakil, S.A., Madkour, M.A. and Abdou, M.A., (2007), Application of Exp-function method for nonlinear evolution equations with variable coefficients, Phys. Lett. A 369, 62-69.
• He, J.H. and Wu, X.H., (2006), Construction of solitary solution and compacton-like solution by variational iteration method, Chaos, Solitons and Fractals 29, 108-113.
• Wu, X.H. and He, J.H., EXP-function method and its application to nonlinear equations, Chaos, Solitons and Fractals (in press), doi:10.1016/j.chaos.2007.01.024.
• He, J.H. and Abdou, M.A., (2007), New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals, 34, 1421-1429.
• Zhu, S.D., (2007), Exp-function method for the discrete mKdV lattice, International Journal of Non- linear Sciences and Numerical Simulation 8(3), 465-468.
• Wang, Q., Chen, Y. and Zhang, H., (2005), A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation. Chaos, Solitons and Fractals , 25, 101928.
• Hong, K.Z. et al., (2003), Painleve analysis and some solutions of (2 + 1)-dimensional generalized Burgers equations. Commun Theor Phys, 39, 3934.
• Tang, X.Y. and Lou, S., (2003), Variable separation solutions for the (2 + 1)-dimensional Burgers equations. Chin Phys Lett., 20(3), 335.