A Method of Solving the Periodic Problem for the KDV Equation and Its Generalization

Abstract

We consider a translation invariant evolution equation of the form

$$ \dot u = K[u],({u^1}; = \frac{{\partial u}}{{\partial x}},\dot u = \frac{{\partial u}}{{\partial x}})$$

(10.1)

where u is a vector-function of a continuous variable x or of a discrete variable n; the equation (10.1) is invariant with respect to translations in x (or n).