Summary: We derive and study a hierarchy of nonlinear coupled evolution equations (among which is the coupled Korteweg-de Vries-Schrödinger equation) for which we prove that some mixed initial-boundary value problem is solvable. We give the method of solution together with the Bäcklund transformation and establish the infinite set of conserved densities. We finally discuss the applicability of such equations in plasma physics and hydrodynamics.