Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations

In this paper, the improved Jacobian elliptic function expansionapproach is extended and applied to constructing discrete solutionsof the semi-discrete coupled modified Korteweg de Vries (mKdV)equations with the aid of the symbolic computation system Maple.Some new discrete Jacobian doubly periodic solutions are obtained.When the modulus $m rightarrow 1$, these doubly periodic solutionsdegenerate into the corresponding solitary wave solutions, includingkink-type, bell-type and other types of excitations.