Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P$_{34}$ and P$_3$

V. E. Adler; M. P. Kolesnikov

doi:10.1063/5.0156409

paper

Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P $_{34}$ and P $_{3}$

arXiv:2304.11590 · doi:10.1063/5.0156409

Abstract

We study reductions of the Korteweg--de Vries equation corresponding to stationary equations for symmetries from the noncommutative subalgebra. An equivalent system of $n$ second-order equations is obtained, which reduces to the Painlevé equation P $_{34}$ for $n = 1$ . On the singular line $t = 0$ , a subclass of special solutions is described by a system of $n - 1$ second-order equations, equivalent to the P $_{3}$ equation for $n = 2$ . For these systems, we obtain the isomonodromic Lax pairs and Bäcklund transformations which form the group $Z_{2}^{n} \times Z^{n}$ .

11 pages

References in corpus (1)

The Hamiltonian Structure of the Second Painleve Hierarchy

Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P34​ and P3​

Abstract

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Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P $_{34}$ and P $_{3}$