P. Vojcak

activity

20102023

most citedSymmetry reductions and exact solutions of Lax integrable

3

-dimensional systems

34 citations · 105 across the 14 of their papers we have counts for

collaborators

14 papers

nlin.SI2023

On recursion operators for full-fledged nonlocal symmetries of the reduced quasi-classical self-dual Yang-Mills equation

Jirina Jahnova, Petr Vojcak

We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang-Mills equation. It turns o…

nlin.SI2022

Non-Abelian covering and new recursion operators for the 4D Martínez Alonso-Shabat equation

Petr Vojcak

We present new recursion operators for (shadows of nonlocal) symmetries of the 4D Martínez Alonso-Shabat equation $u_{t y} = u_{z} u_{x y} - u_{y} u_{x z}$ , and we show that their actions…

nlin.SI2020★ 1 cited

On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation

I. S. Krasil'shchik, P. Vojcak

We consider the 4D Mart\'ınez Alonso-Shabat equation $u_{t y} = u_{z} u_{x y} - u_{y} u_{x z}$ (also referred to as the universal hierarchy equation) and using its known Lax pair construc…

nlin.SI2019★ 17 cited

Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation

I. S. Krasil'shchik, O. I. Morozov, P. Vojčák

We study the Veronese web equation $u_{y} u_{t x} + λ u_{x} u_{t y} - (λ + 1) u_{t} u_{x y} = 0$ and using its isospectral Lax pair construct two infinite series of nonlocal conservation laws. In t…

nlin.SI2017★ 2 cited

Reductions of the universal hierarchy and rdDym equations and their symmetry properties

P. Holba, I. S. Krasil'shchik, O. I. Morozov +1

We consider the equations $u_{y y} = u_{y} u_{xx} - (u_{x} + u) u_{x y} + u_{x} u_{y}$ and $u_{y y} = (u_{x} + x) u_{x y} - (u_{xx} + 2) u_{y}$ that arise as reductions of the universal hierarchy and…

nlin.SI2017★ 4 cited

2D reductions of the equation $u_{y y} = u_{t x} + u_{y} u_{xx} - u_{x} u_{x y}$ and their nonlocal symmetries

P. Holba, I. S. Krasil'shchik, O. I. Morozov +1

We consider the 3D equation $u_{y y} = u_{t x} + u_{y} u_{xx} - u_{x} u_{x y}$ and its 2D reductions: (1) $u_{y y} = (u_{y} + y) u_{xx} - u_{x} u_{x y} - 2$ (which is equivalent to the Gibbons-Tsarev equ…

nlin.SI2016★ 8 cited