We present some approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). Some requirements on the form of the solutions and effects of Earth’s rotation and bottom friction are made. The resulting solutions are obtained by solving ODE systems. The corresponding free surfaces are first- or second-order ones. Some conditions of finiteness and localization of the flow are analyzed. The solutions are used to verify the numerical algorithm of the large-particle method. The efficiency of the method is discussed in tests on wave run-up on shore structures.

中文翻译：

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理想化盆地水振荡问题浅水方程组的精确解及其在验证某些数值算法中的应用

我们提出了一些解决抛物面盆地中浅水振荡问题的方法（包括水平面的额外情况）。对解决方案的形式以及地球自转和底部摩擦的影响提出了一些要求。通过解决ODE系统获得最终的解决方案。相应的自由表面是一阶或二阶的。分析了流动的有限性和局部化的一些条件。该解用于验证大粒子法的数值算法。该方法的效率在岸上结构波浪传播测试中进行了讨论。