In the physics field of scattering theory, the inverse scattering problem is that of determining characteristics of an object (its shape, internal constitution, etc.) based on data of how it scatters incoming radiation or particles.
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 Schrödinger equation, the Korteweg–de Vries equation and the KP equation.
The inverse scattering problem is the inverse problem to the direct scattering problem, which is to determine how radiation or particles are scattered based on the characteristics of the scatterer.
Since its early statement for radiolocation, many applications have been found for inverse scattering techniques, including echolocation, geophysical survey, nondestructive testing, medical imaging, quantum field theory.
See also: Inverse scattering transformFamous quotes containing the words inverse, scattering and/or problem:
“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)
“A committee is organic rather than mechanical in its nature: it is not a structure but a plant. It takes root and grows, it flowers, wilts, and dies, scattering the seed from which other committees will bloom in their turn.”
—C. Northcote Parkinson (1909–1993)
“It is very comforting to believe that leaders who do terrible things are, in fact, mad. That way, all we have to do is make sure we don’t put psychotics in high places and we’ve got the problem solved.”
—Tom Wolfe (b. 1931)