Abstract

Solutions are considered for the system of nonlinear equations of a one-dimensional isentropic gas flow with low densities. A typical singularity of these solutions corresponding to a cusp catastrophe is described. A model solution with such a singularity was obtained for the special case of shallow-water equations. Within the terms of this model solution, an asymptotic solution is obtained for the system of nonlinear equations of a one-dimensional isentropic gas flow.

中文翻译：

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一维等熵气流方程解的典型下降尖点奇异性

摘要

考虑低密度一维等熵气流非线性方程组的解。描述了这些解决方案与尖峰灾难对应的典型奇点。对于浅水方程的特殊情况，获得了具有这种奇异性的模型解。在该模型解的范围内，获得了一维等熵气流非线性方程组的渐近解。