Higher order poles in the Belinskii-Zakharov inverse scattering method

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We analyze the possibility of extending the inverse scattering technique of Belinskii and Zakharov to include higher order poles in the scattering matrix. We find that a part of the original construction is inapplicable in a direct fashion. In particular, we show that the treatment of this issue by Francaviglia and Sgarra is incorrect, and their claimed solutions do not indeed solve the Einstein equations. The same result applies to the Papadopoulos construction for SU(n) Yang-Mills fields. We propose a construction to include higher order poles without inconsistencies, but it proves to be much more involved than the simple pole case. We present an explicit solution with a second order pole built by coalescence of a two-first-order-poles metric. © 1988.

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Physics Letters A

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