P. Vojcak

activity

20102020

u_{y y} = u_{t x} + u_{y} u_{xx} - u_{x} u_{x y}

and their nonlocal symmetries

4 citations · 7 across the 4 of their papers we have counts for

collaborators

5 papers

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

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.SI2010

Reciprocal link among the Qiao-Liu peakon equation and the modified Korteweg-de Vries equation

Petr Vojcak

This paper has been withdrawn by the author. The result is already known.