In mathematics and physics, the inverse scattering problem is the problem of determining characteristics of an object, based on data of how it
scatters incoming radiation or particles. It is the
inverse problem to the direct scattering problem, which is to determine how radiation or particles are scattered based on the properties of the scatterer.
Soliton equations are a class of
partial differential equations which can be studied and solved by a method called the
inverse scattering transform, which reduces the nonlinear PDEs to a linear inverse scattering problem. The
nonlinear Schrödinger equation, the
Korteweg–de Vries equation and the
KP equation are examples of soliton equations. In one space dimension the inverse scattering problem is equivalent to a
Riemann-Hilbert problem.
Since its early statement for
radiolocation
Radiolocation, also known as radiolocating or radiopositioning, is the process of finding the location of something through the use of radio waves. It generally refers to passive uses, particularly radar—as well as detecting buried cables, w ...
, many applications have been found for inverse scattering techniques, including
echolocation,
geophysical survey,
nondestructive testing
Nondestructive testing (NDT) is any of a wide group of analysis techniques used in science and technology industry to evaluate the properties of a material, component or system without causing damage.
The terms nondestructive examination (NDE), n ...
,
medical imaging
Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to rev ...
,
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
.
References
* .
* ''Inverse Acoustic and Electromagnetic Scattering Theory''; Colton, David and Kress, Rainer
Scattering theory
Scattering, absorption and radiative transfer (optics)
Inverse problems
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