Additional symmetries for integrable equations and conformal algebra representation
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 \(S^ 1\) 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 \(\lambda^ m\partial_{\lambda}\), with integer m,p. Some additional results about Kac-Moody algebra applications are presented.
integrable nonlinear evolution equations
scientific article; zbMATH DE number 4002691
scientific article