The Initial Boundary Value Problems for a Nonlinear Integrable Equation with 3 × 3 Lax Pair on the Finite Interval

In this paper, we apply Fokas unified method to study the initial boundary value (IBV) problems for nonlinear integrable equation with 3 × 3 Lax pair on the finite interval [0, L ]. The solution can be expressed by the solution of a 3 × 3 Riemann-Hilbert (RH) problem. The relevant jump matrices are written in terms of matrix-value spectral functions s ( k ), S ( k ), S l ( k ), which are determined by initial data at t = 0, boundary values at x = 0 and boundary values at x = L , respectively. What’s more, since the eigenvalues of 3 × 3 coefficient matrix of k spectral parameter in Lax pair are three different values, search for the path of analytic functions in RH problem becomes a very interesting thing.