On the linearizable initial–boundary value problems for the Sasa–Satsuma equation on the half-line

Abstract

The solutions u(x,t) of the Sasa–Satsuma equation was constructed in terms of the solution of a 3 × 3 Riemann–Hilbert problem by Fokas method. To formulate the associated Riemann–Hilbert problem, we need know all of the boundary value data, i.e. u(0,t),ux(0,t),uxx(0,t). However, for a well-posed problem, not all of these boundary data were prescribed, the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In this paper, we analyze particular linearizable boundary conditions, which means all the spectral functions can be constructed by an algebraic system in terms of the initial value data and the predicted boundary value data.