Additional symmetries for integrable equations and conformal algebra representation

✍ Scribed by A. Yu. Orlov; E. I. Schulman

• Publisher: Springer
• Year: 1986
• Tongue: English
• Weight: 336 KB
• Volume: 12
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00416506

✦ Synopsis

We present a regular procedure for constructing an infinite set of additional (spacetime variables explicitly dependent) symmetries of integrable nonlinear evolution equations (INEEs). In our method, additional symmetry equations arise together with their L-A pairs, so that they are integrable themselves. This procedure is based on a modified 'dressing' method. For INEEs in 1 + 1 dimensions, some appropriate symmetry equations are shown to form the vector fields on a circle S ~ algebra representation. In contrast to the so-called isospectral deformations, these symmetries result from conformal transformations of the associated linear problem spectrum. For INEEs in 2 + 1 dimensions, the commutation relations for symmetry equations are shown to coincide with operators 2"~, with integer m,p. Some additional results about Kac-Moody algebra applications are presented.