In this paper, we consider quasilinear hyperbolic system of balance laws describing one-dimensional nonhomogeneous shallow water equations with generalized Riemann initial data. We obtain exact solutions to the shallow water equations with friction by using differential constraint method. A special case of the obtained solution provides well known rarefaction wave to the homogeneous case of the governing equations. We construct a convenient example for the generalized Riemann problem and study the behavior of the solution profiles.

中文翻译：

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非齐次浅水方程广义Riemann问题的精确解

在本文中，我们考虑用广义黎曼初始数据描述一维非均质浅水方程组的平衡律的拟线性双曲系统。利用微分约束方法，我们得到了具有摩擦力的浅水方程的精确解。所获得解决方案的一个特殊情况为控制方程的齐次情况提供了众所周知的稀疏波。我们为广义Riemann问题构建了一个方便的示例，并研究了解决方案配置文件的行为。