ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
It is shown how to invert the Zakharov-Shabat eigenvalue problem for rational scattering coefficients, in order to produce potentials defined over the whole real line. The method reduces the problem to finding two semi-infinite potentials—which can be efficiently calculated using the soliton-lattice algorithm described in a previous paper. The inversion is usually unique for given rational scattering coefficients, since they usually specify the scattering data of the system uniquely. In the case of nonunique inversion, it is possible to obtain a family of potentials from the inversion. Each member of the family has the same scattering data, except for differing residues. Examples of the inversion include an ‘adiabatic' inversion pulse for use in nuclear magnetic resonance, and a demonstration of how the cubic nonlinear Schrödinger equation may be integrated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530617
