TY - JOUR

T1 - Inverse Scattering on the Line—an Overview

AU - Deift, Percy

N1 - Funding Information:
author also acknowledges the support of NSF grant# DMS-8802305, and of the Institute for Advanced Studies, Princeton.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - This chapter describes the inverse scattering on the line. Historically interest in inverse scattering theory began with the frustration of theoretical physicists in trying to construct a rigorous quantum field theory. This “existential” theory took the name S-matrix theory. Using a technique which the chapter refers to as Darboux transformations, or Backlund transformations, by example that h was not determined by S(h). Thus S-matrix theory was indeed weaker than the Hamiltonian theory. Four major technical problems arise, the first in the direct scattering theory, the remaining three in the inverse theory.

AB - This chapter describes the inverse scattering on the line. Historically interest in inverse scattering theory began with the frustration of theoretical physicists in trying to construct a rigorous quantum field theory. This “existential” theory took the name S-matrix theory. Using a technique which the chapter refers to as Darboux transformations, or Backlund transformations, by example that h was not determined by S(h). Thus S-matrix theory was indeed weaker than the Hamiltonian theory. Four major technical problems arise, the first in the direct scattering theory, the remaining three in the inverse theory.

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U2 - 10.1016/S0076-5392(08)63375-5

DO - 10.1016/S0076-5392(08)63375-5

M3 - Article

AN - SCOPUS:31844446643

VL - 186

SP - 45

EP - 62

JO - Mathematics in Science and Engineering

JF - Mathematics in Science and Engineering

SN - 0076-5392

IS - C

ER -