A particular N-soliton solution and scalar wave equations

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Abstract
A special class of N‐soliton solutions of the Korteweg–deVries equation is examined. It is shown that the nonscattering wave equation based on the corresponding special reflectionless potentials can be obtained by a coordinate transformation of the ordinary wave equation and that these reflectionless potentials and others occur in the scalar wave equation on black hole geometries of general relativity.