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

TL;DR

This paper develops an elliptic direct linearisation scheme for the lattice CKP equation, enabling the construction of elliptic solutions and continuum limits, advancing the understanding of integrable lattice equations.

Contribution

It introduces a novel elliptic direct linearisation scheme and provides explicit elliptic multi-soliton solutions for the lattice CKP equation.

Findings

Elliptic solutions are explicitly constructed.

Continuum limits of the lattice CKP equation are derived.

Elliptic multi-soliton solutions are obtained.

Abstract

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.