INITIAL-BOUNDARY VALUE-PROBLEMS AND DARBOUX-LEVI-TYPE TRANSFORMATIONSASSOCIATED WITH A 2-DIMENSIONAL EIGENFUNCTION EQUATION(1)

The non-linear eigenfunction equation for the integrable 2 + 1-dimensi onal Sawada-Kotera equation is shown to admit a linear decomposition b y virtue of a Lax representation. Classes of initial/boundary value pr oblems are thereby solved on the half-planes -infinity < x < infinity, y greater than or equal to 0 and -infinity < y < infinity, x greater than or equal to 0 respectively. A Darboux-Levi theorem is presented w hereby associated solutions of the 2 + 1-dimensional Sawada-Kotera equ ation may be constructed.