P. A. Treharne

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We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3× 3 matrix Fuchs–Garnier pairs for the third, fourth, and fifth Painlevé equations, together with the previously known Fuchs–Garnier pair for the sixth Painlevé equation. These Fuchs–Garnier pairs have an important(More)
We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system, to its Lax pair. Thus we obtain new 3×3 matrix Fuchs–Garnier pairs for the third and fifth Painlevé equations, together with the previously known Fuchs– Garnier pair for the fourth and sixth Painlevé equations. These Fuchs–Garnier pairs have an important(More)
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