On the theory of recursion operator
The recursion operator plays a central role in the theory of nonlinear equations integrable by the inverse scattering method. It generates a whole family of equations integrable by a given spectral problem, starting from a given one. For example, for the famous KdV equation this family is given by (KdV equation corresponds to \(n=1)\) \[ \partial_ tu+\partial_ xL^ nu=0;\quad L=\partial^ 2_ x+2u+2\partial_ x^{-1}\cup \partial,\quad n=1,2,3,.... \] The recursion operator also plays a central role in the Hamilton formulation of the theory of integrable equations. The paper under review contains significant results concerning the theory of the recursion operator associated to Hamiltonian equations. In particular a method of writing down the recursion operator for nonlinear waves in arbitrary dimensions is proposed.
scientific article; zbMATH DE number 3955578
scientific article