A Nonlinear Difference Scheme and Inverse Scattering
Authors:
- 28 September 1976
- journal article
- research article
- Published by Wiley in Studies in Applied Mathematics
- Vol. 55 (3) , 213-229
Abstract
A nonlinear partial difference equation is obtained and solved by the method of inverse scattering. In a certain continuum limit it is shown how this equation approximates the nonlinear Schrodinger equation and a related nonlinear differential‐difference equation. At all times the solutions can be compared, and the scheme is shown to be convergent. These ideas apply to other nonlinear evolution equations as well.Keywords
This publication has 6 references indexed in Scilit:
- On Some Periodic Toda LatticesProceedings of the National Academy of Sciences, 1975
- Nonlinear differential−difference equationsJournal of Mathematical Physics, 1975
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear ProblemsStudies in Applied Mathematics, 1974
- On the Toda Lattice. II: Inverse-Scattering SolutionProgress of Theoretical Physics, 1974
- On discrete inverse scattering problems. IIJournal of Mathematical Physics, 1973
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967