Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
نویسندگان
چکیده
منابع مشابه
v 2 3 0 M ar 2 00 4 Partner symmetries and non - invariant solutions of four - dimensional heavenly equations
We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to syst...
متن کامل0 40 30 20 v 1 1 2 M ar 2 00 4 Partner symmetries and non - invariant solutions of four - dimensional heavenly equations
We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to syst...
متن کاملar X iv : m at h - ph / 0 40 30 20 v 3 2 8 Ju l 2 00 4 Partner symmetries and non - invariant solutions of four - dimensional heavenly equations
We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equat...
متن کاملSymmetries and Group-invariant Solutions of Nonlinear Fractional Differential Equations
In the paper, methods of Lie group analysis are applied to investigate symmetry properties of some classes of nonlinear fractional differential equations. For class of equations Dy = f(x, y), 0 < α < 1, the problem of group classification is solved. Symmetry properties of equations D t u = (k(u)ux)x, 0 < α ≤ 2 for different orders of α are compared. Obtained symmetries are used to construct exa...
متن کاملOn a class of second-order PDEs admitting partner symmetries
Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebañski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs with four variables, that possess partner symmetries and contain only second derivatives of the unknown. We present recursion relations for symmetries for thes...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2004
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/37/30/010