The Eckhaus equation on the semiline: a Cauchy problem

Abstract: The Cauchy problem with a mixed boundary condition on the semiline for the so-called Eckhaus equation (a generalized form of the nonlinear Schroedinger equation) is solved, i.e. reduced to a linear integral equation in one independent variable. This integral equation is then reduced to the Neumann series by Picard's method of successive approximations, in a numerical example.