Coherent states, inverse mapping formula for Weyl transformations and application to equations of KdV type (Q1173664)

Any continuous linear operator from \({\mathcal S}(R)\) to \({\mathcal S}'(R)\) is called generalized operator. The inverse Weil transform is computed for such operators. The obtained assertions are used to prove that some nonlinear partial differential equations are generalized Korteweg-de Vries (KdV) type equations.