In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furthermore, we study the interaction between simple waves in detail through exact solution of general initial value problem. Finally, we discuss the all possible interaction of elementary waves using the solution of Riemann problem.

中文翻译：

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宏观生产模型中的非线性波相互作用

在本文中，我们研究了控制宏观生产的准线性双曲型偏微分方程（PDE）的2×2齐次系统的非线性波相互作用的详尽分析。我们使用全息图变换和微分约束技术来获得控制方程的精确解。此外，我们通过精确求解一般初值问题来详细研究简单波之间的相互作用。最后，我们使用黎曼问题的解决方案讨论了基波的所有可能相互作用。