Abstract
The coupled modified KdV lattice equation is a discrete version of the coupled modified KdV equation. This paper presents the general formulae for the higher‐order rational, semi‐rational, and mixed soliton solutions in terms of determinants by constructing the generalized perturbation ‐fold Darboux transformation. Particularly, we exhibit the first‐, second‐, and third‐order rational and semi‐rational soliton solutions. Finally, numerical simulations are carried out to explore the dynamical behaviors and instability of those discrete rational and semi‐rational soliton solutions, respectively. The results would enrich our understanding on the two‐layered fluid waves near ocean shores described by the coupled modified KdV lattice equation.
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