Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method
This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
<p>[1] R. Jiwari, S. Pandit, R. C. Mittal. Numerical Simulation Of two -
dimensional Sine-Gorden solitons by differential quadrature method,
Computer Physics Communciation, vol. 183,2012, pp. 600-616.
[2] K. A. Gapreel, A Generalized (G'/G)-expansion method to find the
traveling wave solutions of nonlinear evolution equations, Journal of
Partial Differential Equations, vol. 24, 2011, pp. 55-69.
[3] A. A. Mohammad and M. Can, Painlev´e Analysis and Symmetries of the
HirotaSatsuma Equation, Nonlinear Mathematical Physics, vol. 3, 1996,
pp. 152-155.
[4] S. Zhang and H. Q. Zhang, Discrete Jacobi elliptic function expansion
method for nonlinear differential-difference equations, Physica Scripta,
vol. 80, 2009, pp. 045002.
[5] M. Wang, X. Li, J. Zhang, The (G'/G)-expansion method and travelling
wave solutions of nonlinear evolution equations in mathematical physics,
Physics Letters A, vol. 372, 2008, pp. 417-428.
[6] J. P. Yu and Y. L. Sun, Weierstrass Elliptic Function Solutions to
Nonlinear Evolution Equations, Communication in Theoretical Physics,
vol. 50, 2008, pp. 295-298.
[7] N. Goyal and R. K. Gupta, The On symmetries and exact solution
of Einstein vacuum equations for Axially symmetric Gravitional Fields,
International Journal of Mathematical and Computational Science, vol.
6,2012 pp. 104-107.
[8] B. Han, Promotion (G'/G)-expansion method for solving nonlinear equation.
chifeng college Letters: Natural Science Press (2010).
[9] Sheng Zhang, Ling Dong, Jin-Mei Ba, Ying-Na Sun. The (G'/G)-expansion method for solving nonlinear differential difference equation,
Physics Letters A, vol. 373,2009 pp. 905-910.
[10] Ming Liang Wang, ZhiBing Li,Yu Bing Zhou. The Homogenous Balance
Principal and its Application. Physics Letters of LanZhou University,
vol. 35, 1999, pp. 8-16.
[11] Wang M. , X. Li and J. Zang, (G'/G)-expansion method and travelling
wave solution equation of nonlinear evolution equation in mathematical
physics. Physics.Lett.A, vol. 372, 2008, pp. 417-423.
[12] W. Malfielt and W. Hereman, The tanh method: I. Exact solutions of
nonlinear evolution and wave equations, Physica Scripta, vol. 54, 1996,
pp. 563-568.</p>
<p>[1] R. Jiwari, S. Pandit, R. C. Mittal. Numerical Simulation Of two -
dimensional Sine-Gorden solitons by differential quadrature method,
Computer Physics Communciation, vol. 183,2012, pp. 600-616.
[2] K. A. Gapreel, A Generalized (G'/G)-expansion method to find the
traveling wave solutions of nonlinear evolution equations, Journal of
Partial Differential Equations, vol. 24, 2011, pp. 55-69.
[3] A. A. Mohammad and M. Can, Painlev´e Analysis and Symmetries of the
HirotaSatsuma Equation, Nonlinear Mathematical Physics, vol. 3, 1996,
pp. 152-155.
[4] S. Zhang and H. Q. Zhang, Discrete Jacobi elliptic function expansion
method for nonlinear differential-difference equations, Physica Scripta,
vol. 80, 2009, pp. 045002.
[5] M. Wang, X. Li, J. Zhang, The (G'/G)-expansion method and travelling
wave solutions of nonlinear evolution equations in mathematical physics,
Physics Letters A, vol. 372, 2008, pp. 417-428.
[6] J. P. Yu and Y. L. Sun, Weierstrass Elliptic Function Solutions to
Nonlinear Evolution Equations, Communication in Theoretical Physics,
vol. 50, 2008, pp. 295-298.
[7] N. Goyal and R. K. Gupta, The On symmetries and exact solution
of Einstein vacuum equations for Axially symmetric Gravitional Fields,
International Journal of Mathematical and Computational Science, vol.
6,2012 pp. 104-107.
[8] B. Han, Promotion (G'/G)-expansion method for solving nonlinear equation.
chifeng college Letters: Natural Science Press (2010).
[9] Sheng Zhang, Ling Dong, Jin-Mei Ba, Ying-Na Sun. The (G'/G)-expansion method for solving nonlinear differential difference equation,
Physics Letters A, vol. 373,2009 pp. 905-910.
[10] Ming Liang Wang, ZhiBing Li,Yu Bing Zhou. The Homogenous Balance
Principal and its Application. Physics Letters of LanZhou University,
vol. 35, 1999, pp. 8-16.
[11] Wang M. , X. Li and J. Zang, (G'/G)-expansion method and travelling
wave solution equation of nonlinear evolution equation in mathematical
physics. Physics.Lett.A, vol. 372, 2008, pp. 417-423.
[12] W. Malfielt and W. Hereman, The tanh method: I. Exact solutions of
nonlinear evolution and wave equations, Physica Scripta, vol. 54, 1996,
pp. 563-568.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62878", author = "Anjali Verma and Ram Jiwari and Jitender Kumar", title = "Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method", abstract = "This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.
", keywords = "Shallow water wave equation, Exact solutions, (G'/G) expansion method.", volume = "7", number = "5", pages = "865-5", }
