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.

在本文中，我们应用Fokas统一方法研究有限区间[0, L ]上具有3 × 3 Lax对的非线性可积方程的初边值(IBV)问题。该解可以用 3 × 3 黎曼-希尔伯特 (RH) 问题的解来表示。相关的跳跃矩阵用矩阵值谱函数s ( k ), S ( k ), S _l ( k ) 表示，它们由t = 0处的初始数据、x = 0 处的边界值和边界值决定在x = L， 分别。更重要的是，由于Lax对中k个谱参数的3×3系数矩阵的特征值是三个不同的值，在RH问题中寻找解析函数的路径就成了一件很有趣的事情。