A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation
作者： Yafeng Xiao , Haili Xue , Hongqing Zhang
DOI: 10.1155/2012/896748
关键词: Elliptic function 、 Mathematical analysis 、 Mathematics 、 Jacobi elliptic functions 、 Partial differential equation 、 Jacobi method 、 Cnoidal wave 、 Wave equation 、 Elliptic integral 、 Laurent series
摘要: With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means ansatz, in which periodic solutions nonlinear evolution equations, can be expressed as finite Laurent series some 12 functions, are very effective to uniformly construct more exact terms partial differential equations. As an application method, we choose generalized shallow water wave (GSWW) equation illustrate method. result, successfully obtain solutions. Of course, shock or solitary gotten at their limit condition.
hindawi.com参考文章(35)
J. Hietarinta, Hirota’s Bilinear Method and Partial Integrability Springer Netherlands. pp. 459- 478 ,(1990) , 10.1007/978-94-009-0591-7_17
VB Matveev, MA Salle, Darboux transformations and solitons ,(1992)
R. Hirota, Direct Methods in Soliton Theory Solitons. Series: Topics in Current Physics. ,vol. 17, pp. 157- 176 ,(1980) , 10.1007/978-3-642-81448-8_5
Sen-yue Lou, Jizong Lu, Special solutions from the variable separation approach: the Davey - Stewartson equation Journal of Physics A. ,vol. 29, pp. 4209- 4215 ,(1996) , 10.1088/0305-4470/29/14/038
Partially Intergrable Evolution Equations in Physics Kluwer Academic Publishers. ,(1990) , 10.1007/978-94-009-0591-7
Mark J. Ablowitz, David J. Kaup, Alan C. Newell, Harvey Segur, The Inverse scattering transform fourier analysis for nonlinear problems Studies in Applied Mathematics. ,vol. 53, pp. 249- 315 ,(1974) , 10.1002/SAPM1974534249
S.A. Elwakil, S.K. El-Labany, M.A. Zahran, R. Sabry, Modified extended tanh-function method and its applications to nonlinear equations Applied Mathematics and Computation. ,vol. 161, pp. 403- 412 ,(2005) , 10.1016/J.AMC.2003.12.035
P A Clarkson, E L Mansfield, On a Shallow Water Wave Equation Nonlinearity. ,vol. 7, pp. 975- 1000 ,(1994) , 10.1088/0951-7715/7/3/012
Zhenya Yan, New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations Physics Letters A. ,vol. 292, pp. 100- 106 ,(2001) , 10.1016/S0375-9601(01)00772-1
Peter A. Clarkson, Martin D. Kruskal, New similarity reductions of the Boussinesq equation Journal of Mathematical Physics. ,vol. 30, pp. 2201- 2213 ,(1989) , 10.1063/1.528613