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On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ xxx + 6 Qψ x + 6 R ψ = λ ψ
Author(s) -
Kaup D. J.
Publication year - 1980
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/sapm1980623189
Subject(s) - inverse scattering problem , eigenvalues and eigenvectors , scattering , infinity , mathematics , inverse , mathematical analysis , inverse problem , inverse scattering transform , class (philosophy) , spectrum (functional analysis) , soliton , mathematical physics , scattering theory , combinatorics , physics , quantum mechanics , geometry , nonlinear system , computer science , artificial intelligence
The inverse scattering problem for cubic eigenvalue equations of the form ψ xxx + 6 Qψ x + 6 R ψ = λ ψ is outlined and formally solved. Many properties of the scattering data are obtained, the continuous spectrum is briefly discussed, special one soliton solutions are obtained, and the infinity of conserved quantities are determined in terms of the scattering data.