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@book{60752,
author = {Baran, Hynek},
keywords = {Integrable systems; Nonlocal symmetries; Recursion operators; partial differential equation; integrable linearity degenerate equation; nonlocal symmetry; recursion operator; three-dimensional rdDym equation; symmetry reductions; solutions; the Gibbons-Tsarev equation; Lax-integrable equations},
language = {eng},
title = {Integrabilita a geometrie},
year = {2021}
}
TY -
ID - 60752
AU - Baran, Hynek
PY - 2021
TI - Integrabilita a geometrie
KW - Integrable systems
KW - Nonlocal symmetries
KW - Recursion operators
KW - partial differential equation
KW - integrable linearity degenerate equation
KW - nonlocal symmetry
KW - recursion operator
KW - three-dimensional rdDym equation
KW - symmetry reductions
KW - solutions
KW - the Gibbons-Tsarev equation
KW - Lax-integrable equations
N2 - Different approaches to integrability of partial differential equations (pdes) are based on their diverse but related properties such as existence of infinite hierarchies of (local or nonlocal) symmetries and/or conservation laws, zero-curvature representations, Lax integrability, recursion operators etc. This thesis consists of papers: [I] Baran, H. Infinitely many commuting nonlocal symmetries for modified Martinez Alonso–Shabat equation. Communications in Nonlinear Science and Numerical Simulation 96 (2021), 105692. [II] Baran, H., Krasil’shchik, I.S., Morozov, O.I., and Vojčák, P. Nonlocal Symmetries of Integrable Linearly Degenerate Equations: A Comparative Study. Theoretical and Mathematical Physics 196 (2)(2018), 1089–1110. [III] Baran, H., Krasil’shchik, I. S., Morozov, O.I., and Vojčák, P. Coverings over Lax integrable equations and their nonlocal symmetries. Theoretical and Mathematical Physics 188 (3)(2016), 1273–1295. [IV] Baran, H., Krasil’shchik, I.S., Morozov, O.I., and Vojčák, P. Integrability properties of some equations obtained by symmetry reductions. Journal of Nonlinear Mathematical Physics 22 (2)(2015), 210–232. [V] Baran, H., Krasil’shchik, I.S., Morozov, O.I., and Vojčák, P. Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems. Journal of Nonlinear Mathematical Physics 21 (4)(2014), 643–671. [VI] Baran, H. and Marvan, M. Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation. Nonlinearity 23 (10) (2010), 2577–2597. [VII] Baran,H. and Marvan, M. On integrability of Weingarten surfaces: A forgotten class. Journal of PhysicsA: Mathematical and Theoretical 42 (40) (2009), 404007. All of them study integrability properties of some or several nonlinear PDE.
ER -
BARAN, Hynek. \textit{Integrabilita a geometrie}. 2021.
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