The minimal Lorentzian surfaces in \(\mathbb {R}^4_2\) whose first normal space is two-dimensional and whose Gauss curvature K and normal curvature \(\varkappa \) satisfy \(K^2-\varkappa ^2 >0\) are called minimal Lorentzian surfaces of general type. These surfaces admit canonical parameters and with respect to such parameters are determined uniquely up to a motion in \(\mathbb {R}^4_2\) by the curvatures K and \(\varkappa \) satisfying a system of two natural PDEs. In the present paper we study minimal Lorentzian surfaces in \(\mathbb {R}^4_2\) and find a Weierstrass representation with respect to isothermal parameters of any minimal surface with two-dimensional first normal space. We also obtain a Weierstrass representation with respect to canonical parameters of any minimal Lorentzian surface of general type and solve explicitly the system of natural PDEs expressing any solution to this system by means of four real functions of one variable.

\（\ mathbb {R} ^ 4_2 \）中其第一法向空间为二维且其高斯曲率K和法向曲率\（\ varkappa \）的最小洛伦兹曲面满足\（K ^ 2- \ varkappa ^ 2> 0 \）称为一般类型的最小洛伦兹曲面。这些曲面允许使用规范参数，并且相对于此类参数，由满足两个自然PDE系统的曲率K和\（\ varkappa \）唯一地确定直至\（\ mathbb {R} ^ 4_2 \）中的运动。在本文中，我们研究\（\ mathbb {R} ^ 4_2 \）中的最小洛伦兹曲面并找到具有二维第一法向空间的任何最小表面的等温参数的Weierstrass表示。我们还获得了关于一般类型的任何最小洛伦兹曲面的规范参数的Weierstrass表示，并通过一个变量的四个实函数来明确求解表示该系统任何解的自然PDE系统。