Dynamics of Partial Differential Equations

Volume 2 (2005)

Number 2

Inner automorphisms, discrete and Bäcklund transformations of integrable systems

Pages: 149 – 158

DOI: https://dx.doi.org/10.4310/DPDE.2005.v2.n2.a3


A. N. Leznov (CIICAP, Universidad Autonoma del Estado de Morelos, Cuernavaca, Mexico)


It is shown that there exist two inner automorphisms and a discrete transformation besides the usual Bäcklund transformation for the integrable focusing nonlinear Schrödinger equation. By virtue of the inner automorphisms, the discrete transformation can generate multi-soliton solutions. The expressions for multi-soliton solutions generated by the discrete and the Bäcklund transformations turn out to be the same.


inner automorphism, discrete transformation, Bäcklund transformation, integrable system, multi-soliton solution

2010 Mathematics Subject Classification

Primary 35-xx. Secondary 78-xx.

Published 1 January 2005