Mathematics

Over the last several months and in a series of papers, S.Y. Lou and collaborators have presented several examples of new (D+1)-dimensional integrable PDEs, obtained by a deformation of known integrable (1 + 1)-dimensional systems. The procedure is called "deformation algorithm" and it can be applied to both evolutionary and non-evolutionary (in this latter case we speak of "generalized deformation algorithm") PDEs. In this talk I will describe the straightforward procedure and prove that it indeed allows to obtain Lax-integrable multidimensional systems by deforming Lax-integrable 1-dimensional systems. This is a joint work with Danda Zhang (Ningbo). Ref: arxiv.org/2305.08449