The inverse spectral problem for indefinite strings by Jonathan Eckhardt, Aleksey Kostenko

“…Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form −u" = z u ω + z2u υ on an interval [0, L), where ω is a real-valued distribution in H −1loc [0, L), υ is a non-negative Borel measure on [0, L) and z is a complex spectral parameter. …”
Get full text