We present three alternative derivations of the method of characteristics (MOC) for a second order nonlinear hyperbolic partial differential equation. The MOC gives rise to two mutually coupled systems of ordinary differential equations. As a special case we consider the Monge-Amp\`ere equation, for which we solve the system of ODE's using explicit one-step methods (Euler, Runge-Kutta) and spline interpolation. Numerical examples demonstrate the performance of the methods.

翻译：我们提出了二阶非线性双曲部分偏差方程式特性方法(MOC)的三种不同推论:MOC产生两个相互结合的普通差分方程式系统。作为一个特殊案例,我们考虑蒙古-安培-埃雷方程式,为此,我们使用明确的一步法(Euler、Runge-Kutta)和样板内插法解决了ODE系统(Euler、Runge-Kutta)和样板内插法。数字示例显示了方法的性能。