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{{Short description|Method for solving certain non-linear partial differential equations}}
In [[mathematics]], the '''inverse scattering transform''' is a method for solving some non-linear [[partial differential equations]]. The method is a non-linear analogue, and in some sense generalization, of the [[Fourier transform]], which itself is applied to solve many linear partial differential equations. The name "inverse scattering method" comes from the key idea of recovering the time evolution of a potential from the time evolution of its scattering data: inverse scattering refers to the problem of recovering a potential from its scattering matrix, as opposed to the direct scattering problem of finding the scattering matrix from the potential.
The inverse scattering transform may be applied to many of the so-called [[exactly solvable model]]s, that is to say [[completely integrable]] infinite dimensional systems.
==Overview==
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