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A Nonlinear Difference Scheme and Inverse Scattering
Author(s) -
Ablowitz M. J.,
Ladik J. F.
Publication year - 1976
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1976553213
Subject(s) - inverse scattering transform , mathematics , nonlinear system , inverse scattering problem , partial differential equation , nonlinear schrödinger equation , mathematical analysis , limit (mathematics) , differential equation , scattering , split step method , first order partial differential equation , schrödinger equation , inverse problem , physics , quantum mechanics
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.