The scattering transform for the two-dimensional Schrodinger operator with a potential that decreases at infinity at fixed nonzero energyстатья
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Дата последнего поиска статьи во внешних источниках: 13 января 2015 г.
Аннотация:We study the problem of reconstructing the potential of the two-dimensional Schrödinger operator from scattering data measured at fixed energy. This problem, in contrast to the general multidimensional inverse problem, possesses an infinite-dimensional symmetry algebra generated by the Novikov-Veselov hierarchy and hence is "exactly soluble" in some sense; the complexity of the answer is approximately the same as in the one-dimensional problem. We make heavy use of methods developed in modern soliton theory. Since the quantum fixed-energy scattering problem is mathematically equivalent to the acoustic single-frequency scattering problem, we see that the results of the present paper apply in both cases.