Lax representations and Bäcklund transformations for one-dimensional nonlinear evolution equations (Q1921767)

The paper presents a discussion of Lax representation of some one-dimensional nonlinear evolution equations and its link to the Bäcklund transformations. In particular, the authors show that two operators \({\mathcal L}\) and \({\mathcal A}\) of the form \({\mathcal L} = AD_{xx} + BD_x + C\) and \({\mathcal A} = {\mathcal D} D_{xx} + ED_x +F\) form a Lax pair for special relations between the coefficients. Most of the results are not original, however, the paper includes detailed proofs.