Problems in implementing the self-consistent profile technique in mode-locking theory

It is shown that, in the case of mode locking by synchronous pumping, the standard method for implementing the self-consistent profile technique has a hidden flaw. The imposition of a functional form of the solution in advance supplies a spurious mathematical constraint leading to incorrect solutions, while the true constraint which is associated with the leading-edge boundary condition on the pulse profile is ignored. Correct solutions are readily obtained by numerical methods.<
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