On the Riemann-Hilbert transformations for a Galilean invariant system (Q1094597)

This paper deals with the Riemann-Hilbert transformations for the solution of a Galilean invariant nonlinear problem. New solutions of the system are derived from the old ones by an algebraic R-H transformation using methods of linear algebra. It is proved that the infinitesimal R-H transformations form a Lie algebra of infinite dimension without making recourse to a series of potentials. This procedure succeeds in an algebra homomorphic to a Kac-Moody Lie algebra without center.