Eur. Phys. J. Plus (2015) 130: 13
https://doi.org/10.1140/epjp/i2015-15013-9

Regular Article

Discrete exact solutions for the double-well potential model through the discrete tanh method

¹ Higher Teachers’ Training College of Maroua, The University of Maroua, Maroua, P.O. Box. 46, Cameroon
² Department of Physics, Faculty of Science, The University of Maroua, Maroua, P.O. Box. 46, Cameroon
³ Department of Physics, Faculty of Science, The University of Yaounde I, Yaounde, P.O. Box. 812, Cameroon
⁴ Centre d’Excellence Africain en Technologie de l’Information et de la Communication, The University of Yaounde I, Yaounde, P.O. Box. 812, Cameroon

^* e-mail: amadougabriel@yahoo.fr

Received: 26 September 2014
Revised: 16 November 2014
Accepted: 16 December 2014
Published online: 29 January 2015

Abstract

In this paper, we investigate discrete exact solutions for the double-well potential model by using the discrete tanh method. As a result, various discrete new solutions are obtained. They include breathers, kink, antikink and periodic waves solutions for different values of the discrete variable n. We also establish conditions for obtaining these types of solutions. The amplitude of these solutions decreases when the discrete variable n increases. The total energy is also calculated for each kind of solutions. Finally, we show, in the comparison with the continuous case, that some of our results where soliton like similar solutions are well known in the literature.