SOLUTION OF 3 WAVES INTERACTION TYPE MODELS WITH NONTRIVIAL ASYMPTOTIC AND BOUNDARY-CONDITIONS

In the following we introduce a new way to solve the Cauchy problem fo r nonvanishing potentials at infinity for the spectral problem of the Zakharov and Shabat, Ablowitz, Kaup, Newell, and Segur (ZS-AKNS) hiera rchy. Then we apply the results to solve a class of coupled systems, w ith this nonvanishing condition on the potential and with quite genera l boundary conditions on the other fields. Finally we present an appli cation to a physical system governed by a three waves interaction type model. (C) 1995 American Institute of Physics.