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.
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