Solution of an initial-boundary value problem for coupled nonlinear waves

Abstract

The authors derive and study a hierarchy of nonlinear coupled evolution equations (among which is the coupled Korteveg-de Vries/Schrodinger equation) for which they prove that a mixed initial-boundary value problem is solvable. They give the method of solution together with the Backlund transformation and establish the infinite set of conserved densities. They finally discuss the applicability of such equations in plasma physics and hydrodynamics.