The general solution for simple harmonic generation is obtained by inverse scattering techniques. The time evolution of the scattering data is found to be much more complicated than in all other cases which are solvable by inverse scattering. It is also pointed out that the instability of the real solutions of simple harmonic generation is related to the singular nature of the scattering data about ζ = 0.
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D. J. Kaup (1978) studied this question.
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