Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P$_{34}$ and P$_3$ (2304.11590v1)

Published 23 Apr 2023 in nlin.SI

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 Painlev\'e 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 B\"acklund transformations which form the group ${\mathbb Z}n_2\times{\mathbb Z}n$.

Summary

We haven't generated a summary for this paper yet.