In this work, the matrix Riemann–Hilbert problem of the pair transition coupled nonlinear Schrödinger (ptcNLS) equations is presented in the complex \(\zeta \)-plane. According to the unique solution of the resulting Riemann–Hilbert problem, the formal soliton solution to the initial value problem of the ptcNLS equations is derived ultimately.

中文翻译：

---

通过Riemann–Hilbert方法求解成对跃迁耦合非线性Schrödinger方程的初值问题

在这项工作中，成对跃迁耦合非线性Schrödinger（ptcNLS）方程的矩阵Riemann-Hilbert问题在复（\ zeta \）-平面中提出。根据所得黎曼-希尔伯特问题的唯一解，最终得出ptcNLS方程初值问题的形式孤子解。