Inverse scattering transform: Difference between revisions

Revision as of 11:52, 10 February 2016

Revision as of 17:13, 15 August 2016

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The inverse scattering problem can be written as a [[Riemann–Hilbert factorization]] problem, at least in the case of equations of one space dimension. This formulation can be generalized to differential operators of order greater than 2 and also to periodic potentials.

In higher space dimensions onone has instead a "nonlocal" Riemann–Hilbert factorization problem (with convolution instead of multiplication) or a d-bar problem.

==Example: the Korteweg–de Vries equation==