The heterogeneous string: coupled helices in Hilbert space
1. We solve the initial-value problem for the partial-differential equation "« s(x)2"** = 0, (11) given u(x, 0) =f(x), u,(x, 0) = g(x); (1.2) in matters of notation, we follow [1], We take as the phase-space for the problem the space of initial data having finite energy, with inner product derived from the energy quadratic form. As in [1], we first straighten the characteristics of (1.1) with the transformation