Skip to main content
NCBI home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1980 Sep;77(9):5025–5027. doi: 10.1073/pnas.77.9.5025

Bäcklund transformations and nonlinear differential difference equations

D Levi 1,*, R Benguria 1,†
PMCID: PMC349985  PMID: 16592867

Abstract

It is shown that any Bäcklund transformation of a nonlinear differential equation integrable by the multichannel Schrödinger eigenvalue problem can be written in the form Vx = 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.

Keywords: nonlinear evolution equations, Schrödinger spectral problem, soliton

Full text

PDF
5025

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES