KdV hierarchy
In mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which starts with the Korteweg–de Vries equation.Details
Let be translation operator defined on real valued functions as. Let be set of all analytic functions that satisfy, i.e. periodic functions of period 1. For each, define an operator
on the space of smooth functions on. We define the Bloch spectrum to be the set of such that there is a nonzero function with and. The KdV hierarchy is a sequence of nonlinear differential operators such that for any we have an analytic function and we define to be and
then is independent of.
The KdV hierarchy arises naturally as a statement of Huygens' principle for the D'Alembertian.
