RAPIDLY FORCED INITIAL-VALUE PROBLEMS

Initial value problems for forced linear and nonlinear partial differe ntial equations are considered where the forcing is assumed to be rapi d compared to the unforced dynamics. A multiscale perturbation method is used to derive solutions in the form of asymptotic expansions. For linear problems, these expansions are equivalent to the integral formu las based on Green's function solutions and thus give a method of expa nding these integral formulas when the kernel is rapidly varying. For nonlinear problems, the method yields new results for which there am n o alternative analytical methods. Several model problems are considere d, including the forced Burgers equation for shock-pulse interactions, the Korteweg-deVries (KdV) equation for forced interacting solitons, and the time-dependent Schrodinger equation with rapidly varying poten tial.