We show that the equation governing pulse propagation in dispersion-managed optical fibers, as well as the reduced form of that equation, does not have conserved or periodically conserved quantities other than the mass, momentum, and (for the reduced equation only) the Hamiltonian. Implications of this result for the problem of four-wave mixing in collisions of pulses in optical telecommunication channels, are discussed.
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Taras I. Lakoba (1999) studied this question.