Inverse scattering problem

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Inverse scattering problem" – news · newspapers · books · scholar · JSTOR (June 2015) (Learn how and when to remove this message)

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.^[1] 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.^[2] Inverse scattering has been applied to many problems including radiolocation, echolocation, geophysical survey, nondestructive testing, medical imaging, quantum field theory.^[3][4]

Citations

References

• Ablowitz, Mark J.; Fokas, A. S. (2003). Complex Variables: Introduction and Applications. Cambridge University Press. pp. 609–613. ISBN 978-0-521-53429-1.

• Bao, Gang (2023). "Mathematical analysis and numerical methods for inverse scattering problems". In Beliaev, D.; Smirnov, S. (eds.). ICM International Congress of Mathematics 2022 July 6-14. EMS Press. p. 5034–5055. ISBN 9783985470587. Retrieved 19 March 2024.Reprint

• Colton, David; Kress, Rainer (2013). Inverse Acoustic and Electromagnetic Scattering Theory. Springer Science & Business Media. ISBN 978-3-662-02835-3.

• Dunajski, Maciej (2010). Solitons, Instantons, and Twistors. OUP Oxford. ISBN 978-0-19-857062-2.

• Grinev, A. Y.; Chebakov, I. A.; Gigolo, A. I. (2003). "Solution of the inverse problems of subsurface radiolocation". International Conference on Antenna Theory and Techniques (Cat. No.03EX699). 2. Sevastopol, Ukraine: 523–526. doi:10.1109/ICATT.2003.1238792.

• Marchenko, V. A. (2011), Sturm-Liouville operators and applications (revised ed.), Providence: American Mathematical Society, ISBN 978-0-8218-5316-0, MR 2798059

This optics-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e

This scattering–related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e

This mathematical physics-related article is a stub. You can help Wikipedia by expanding it.

• v
• t
• e