Fredholm determinants and multiple solitons
- 1 September 1976
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (9) , 1703-1706
- https://doi.org/10.1063/1.523096
Abstract
The discrete inverse scattering problem in one dimension is considered. Exact solutions are obtained using elementary algebraic tools. Expressions found involve determinants of infinite‐dimensional matrices. A simple, heuristic, limiting process yields the solution for the continuous problem. When the reflection coefficients do not contribute (the general N soliton case), the determinants reduce to those of given N×N matrices.Keywords
This publication has 4 references indexed in Scilit:
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- On the Toda Lattice. II: Inverse-Scattering SolutionProgress of Theoretical Physics, 1974
- The discrete inverse scattering problem in one dimensionJournal of Mathematical Physics, 1974
- The soliton: A new concept in applied scienceProceedings of the IEEE, 1973