The construction of canonical separated variables for binary constrained AKNS flow

For separation of variables of a binary constrained flow with 2N degrees of freedom, 2N pairs of canonical variables need to be constructed. The method available can lead to N pairs of canonical separated variables by using its Lax matrix. We propose a new method for introducing N pairs of additional canonical separated variables and additional separated equations. Furthermore, the Jacobi inversion problem for the binary constrained flow is presented.