Integrability in 3+1 Dimensions
by
Igor G. Korepanov
South Ural State University

It is well known that the most general integrable model in 2+1 dimensions is generated by the re-factorizing of a product of 3 block matrices of a special form into the product of similar matrices, but taken in the reverse order. In particular, such models as Hirota and Miwa bilinear equations fit within this approach as some simple cases. Moreover, this approach allows, at least in some cases, an amazingly direct quantization. The similar re-factorizing problem in four dimensions cannot be solved. However, it was discovered recently that there exists a relaxed variant of such problem, which yields perfectly integrable models in 3+1 dimensions.

Date received: December 18, 1997