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An Inverse Problem for the Benney‐Kaup System ‐ Periodic and Decaying Case
Author(s) -
Roy Chowdhury A.,
Purkait Sasanka
Publication year - 1990
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19905020107
Subject(s) - inverse , inverse problem , nonlinear system , mathematical analysis , elliptic function , physics , mathematics , riemann hypothesis , riemann problem , inversion (geology) , mathematical physics , quantum mechanics , geometry , paleontology , structural basin , biology
We have formulated the inverse problem for the Benney‐Kaup system in both the case of asymptotically decaying and periodic solution. In the former we set up the Gelfand‐Levitan‐Marchenko equation and study the analytic properties required therein. In the latter case we prove that the nonlinear field can be determined by the Abel inversion on a Riemann surface with the help of elliptic or theta functions.