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Time Evolution of the Scattering Data for the Forced Toda Lattice
Author(s) -
Wycoff D.,
Kaup D. J.
Publication year - 1989
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/sapm19898117
Subject(s) - inverse scattering transform , toda lattice , scattering , mathematics , mathematical analysis , inverse scattering problem , boundary value problem , lattice (music) , partial differential equation , nonlinear system , scattering theory , inverse problem , physics , integrable system , quantum mechanics , acoustics
Determination of the time evolution of the scattering data for an inverse scattering transform solution of the forced Toda lattice appears to require an overspecification of the boundary condition at the end of the lattice. This appears in the form of an apparent need to specify the values of two functions at the boundary rather than one. We present three different approaches to the resolution of this problem. One approach gives the Maclaurin series (in time) for the scattering data. The second approach gives the scattering data in terms of the solution to a nonlinear, nonlocal partial differential equation. The third approach gives the scattering data in terms of the solution to a linear integral equation. All three approaches reduce to one the number of functions which must be specified to determine a solution. The advantages and limitations of each approach are discussed.