THE SECULAR SOLUTIONS OF THE LINEARIZED KORTEWEG-DE-VRIES EQUATION

We study the inhomogeneous linearized Korteweg-de Vries (KdV) equation . It is solved by the inverse scattering transform method. The secular -producing terms on the right-hand side (rhs) are characterized in sev eral ways: first we give a mathematical characterization as resonant t erms. Second, the secular-producing terms are interpreted as conserved densities of the KdV equation. Third, it is checked that the removal of all linear terms from the rhs, polynomial in the solution of KdV, e nsures the boundness of the solution of the linearized equation. Fourt h, considering this solution itself as the rhs, we determine which par t of it is secular producing, and which part is not. (C) 1998 American Institute of Physics. [S0022-2488(98)03006-0].