Elliptic solutions of the lattice CKP equation and its elliptic direct linearisation scheme

A direct linearisation scheme, based on an elliptic Cauchy kernel, is set up for the lattice CKP equation. This leads to an elliptic parametrisation of the lattice CKP equation, together with its Lax triplet, which allows us to perform appropriate continuum limits and construct elliptic solutions. By selecting appropriate integration measures and domains for the singular linear integral equation in the scheme, elliptic multi-soliton solutions of the lattice CKP equation are found.