可线性化的Abel方程组与Gurevich-Pitaevskii问题
Linearisable Abel equations and the Gurevich--Pitaevskii problem
摘要：
对一类$\mathrm{SL}(2,\mathbb R)$ -不变的三阶常微分方程应用对称约化，得到了其通解可用超几何函数参数化的Abel方程.特殊情况下，这种建设提供了一个一般的参数解的Kudashev方程，常微分方程中产生的Gurevich-Pitaevskii问题，从而使首项的大时间渐近展开的解决方案在振荡（Whitham）区。
英文摘要：
Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb R)$-invariant third-order ODEs, we obtain Abel equations whose general solution can be parametrised by hypergeometric functions. Particular case of this construction provides a general parametric solution to the Kudashev equation, an ODE arising in the Gurevich--Pitaevskii problem, thus giving the first term of a large-time asymptotic expansion of its solution in the oscillatory (Whitham) zone.
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