Eur. Phys. J. Plus (2014) 129: 136
https://doi.org/10.1140/epjp/i2014-14136-9

Regular Article

Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G′/G)-expansion method including the generalized Riccati equation

¹ Laboratory of Mechanics, Department of Physics, Faculty of Sciences, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
² Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, P.O. Box 47, Yaoundé, Cameroon

^* e-mail: tebue2007@gmail.com

Received: 25 May 2014
Accepted: 31 May 2014
Published online: 26 June 2014

Abstract

Using the Jacobi elliptic functions and the alternative (G′/G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.