Bifurcations of new eigenvalues for the Benjamin-Ono equation

A criterion for the emergence of new eigenvalues is found for the linear sc attering problem associated with the Benjamin-Ono (BO) equation. This bifur cation occurs due to perturbations of nongeneric potentials which include t he soliton solutions of the BO equation. The asymptotic approximation of an exponentially small new eigenvalue is derived. The method is based on the expansion of a localized function through a complete set of unperturbed eig enfunctions. Explicit expressions are obtained for the soliton potentials. (C) 1998 American Institute of Physics. [S0022-2488(98)00112-1].