论文信息 - The scaling reduction of the three-wave resonant system and the Painlevé VI equation

The scaling reduction of the three-wave resonant system and the Painlevé VI equation

Abstract The scaling invariant solutions of the three-wave resonant system in one spatial and one temporal dimension satisfy a system of three first-order nonlinear ordinary differential equations. These equations can be reduced to one second-order equation quadratic in the second derivative. This equation is outside the class of equations classified by Painleve and his school. However, it is a special case of an equation recently found to be related via a one-to-one transformation to the Painleve VI equation.

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