Open AccessBäcklund transformations and nonlinear differential difference equations
Author(s) -
Decio Levi,
Rafael D. Benguria
Publication year - 1980
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.77.9.5025
Subject(s) - integrable system , eigenvalues and eigenvectors , mathematics , transformation (genetics) , nonlinear system , differential equation , mathematical analysis , soliton , mathematical physics , differential (mechanical device) , physics , quantum mechanics , chemistry , biochemistry , gene , thermodynamics
It is shown that any Bäcklund transformation of a nonlinear differential equation integrable by the multichannel Schrödinger eigenvalue problem can be written in the formVx =U′V -VU . This allows us to interpret the Bäcklund transformation formally as a nonlinear differential difference equation for which we can immediately construct the soliton solutions.