  A fourth-order multi-exponential scheme is proposed for the Zakharov-Shabat
system. The scheme represents a product of 13 exponential operators. The
construction of the scheme is based on a fourth-order three-exponential scheme,
which contains only one exponent with a spectral parameter. This exponent is
factorized to the fourth-order with the Suzuki formula of 11 exponents. The
obtained scheme allows the use of a fast algorithm in calculating the initial
problem for a large number of spectral parameters and conserves the quadratic
invariant exactly for real spectral parameters.
