Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Sheftel, M. B."'
Autor:
Sheftel, M. B., Yazıcı, D.
Publikováno v:
Communications in Nonlinear Science and Numerical Simulation, Vol. 112 (2022) 106527
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component forms and fin
Externí odkaz:
http://arxiv.org/abs/2109.04111
Autor:
Sheftel, M. B., Yazıcı, D.
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic Monge--Amp\`ere
Externí odkaz:
http://arxiv.org/abs/1804.10620
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian st
Externí odkaz:
http://arxiv.org/abs/1510.03666
Autor:
Sheftel, M. B., Yazıcı, D.
In paper [3] on the classification of second-order PDEs with four independent variables that possess partner symmetries, asymmetric heavenly equation appears as one of canonical equations admitting partner symmetries. It was shown that all these cano
Externí odkaz:
http://arxiv.org/abs/1211.5691
Autor:
Malykh, A. A., Sheftel, M. B.
Publikováno v:
J.Phys.A44:155201,2011
We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov \cite{fer}, governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric governed by the general heavenly equation, null tetrad and basis of 1-fo
Externí odkaz:
http://arxiv.org/abs/1011.2479
Autor:
Sheftel, M. B., Yazici, D.
In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries (J. Phys. A: Math. Theor. Vol. 42 (2009) 395202 (20pp)), mixed heavenly equati
Externí odkaz:
http://arxiv.org/abs/0904.3981
Autor:
Sheftel, M. B., Malykh, A. A.
Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four va
Externí odkaz:
http://arxiv.org/abs/0904.2909
We discover multi-Hamiltonian structure of complex Monge-Ampere equation (CMA) set in a real first-order two-component form. Therefore, by Magri's theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Ha
Externí odkaz:
http://arxiv.org/abs/0802.2203
Autor:
Sheftel, M. B., Malykh, A. A.
We show how partner symmetries of the elliptic and hyperbolic complex Monge-Amp\`ere equations (CMA and HCMA) provide a lift of non-invariant solutions of three- and two-dimensional reduced equations, i.e., a lift of invariant solutions of the origin
Externí odkaz:
http://arxiv.org/abs/0802.1463
Autor:
Nutku, Y., Sheftel, M. B.
We discover Hamiltonian structure of the complex Monge-Amp`ere equation when written in a first order two-component form. We present Lagrangian and Hamiltonian functions, a symplectic form and the Hamiltonian operator that determines the Poisson brac
Externí odkaz:
http://arxiv.org/abs/0801.2663