论文标题
可线化的亚伯方程和gurevich-pitaevskii问题
Linearisable Abel equations and the Gurevich--Pitaevskii problem
论文作者
论文摘要
将对称性还原应用于$ \ mathrm {sl}（2，\ mathbb r）$ - 不变的三阶ODES的类别，我们获得了ABEL方程，其一般解决方案可以通过超几型函数进行参数化。该构建的特殊情况为Kudashev方程提供了一种一般的参数解决方案，Kudashev方程是Gurevich-pitaevskii问题中产生的颂歌，因此给出了其在振荡（WHITHAM）区域中大量渐近扩展的第一项。
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.
