3 × 3 Lax pairs for the fourth , fifth and sixth Painlevé equations
نویسندگان
چکیده
We obtain 3 × 3 matrix Lax pairs for systems of ODEs that are solvable in terms of the fourth, fifth and sixth Painlevé equations by considering similarity reductions of the scattering Lax pair for the (2+1)-dimensional three-wave resonant interaction system. These results allow us to construct new 3× 3 Lax representations for the fourth and fifth Painlevé equations, together with the previously known 3× 3 Lax representation for the sixth Painlevé equation. By comparing these Lax pairs we obtain explicit formulas for the self-similar solutions of the three-wave system in terms of the associated Painlevé equations. Finally, we give a practical application of the 3×3 system associated with the fifth Painlevé equation by using it to derive an Okamoto-type Bäcklund transformation for P5.
منابع مشابه
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