Abstract
Resorting to the finite-order expansion of the Lax matrix, the relation between elliptic coordinates and potentials is established, from which the semi-discrete Chen–Lee–Liu equations are decomposed into solvable ordinary differential equations. Based on the theory of algebraic curves, Abel–Jacobi coordinates are introduced to straighten out the continuous flow and discrete flow, by which explicit solutions of the semi-discrete Chen–Lee–Liu equations are obtained in the Abel–Jacobi coordinates.
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