High Quality Content by WIKIPEDIA articles! In mathematical physics, the Marchenko equation is a solution of the inverse scattering problem, when the energy of the input particle is a variable, and the impact parameter b is constant. In physics, in the area of scattering theory, the inverse scattering problem is the problem of determining the characteristics of an object (its shape, internal constitution, etc.) from measurement data of radiation or particles scattered from the object. In mathematics, inverse scattering refers to the determination of the solutions of a set of differential equations based on known asymptotic solutions, that is, on solving the S-matrix. Examples of equations that have been solved by inverse scattering are the Schroedinger equation, the KdV equation and the KP equation.

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