Inverse scattering problem
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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.
Soliton equations can be studied and solved by inverse scattering. Examples are the Nonlinear Schrödinger equation, the Korteweg–de Vries equation and the KP equation. In one space dimension the inverse scattering problem is equivalent to a Riemann-Hilbert problem.
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.
- Marchenko, V. A. (2011), Sturm-Liouville operators and applications (2 ed.), Providence: American Mathematical Society, ISBN 978-0-8218-5316-0, MR 2798059.
Inverse Acoustic and Electromagnetic Scattering Theory, Colton, David, Kress, Rainer http://www.springer.com/mathematics/dynamical+systems/book/978-1-4614-4941-6
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