Bäcklund transformation of Painlevé III(D8)τfunction
نویسندگان
چکیده
منابع مشابه
Bäcklund Transformations for Fourth Painlevé Hierarchies Pilar
Bäcklund transformations (BTs) for ordinary differential equations (ODEs), and in particular for hierarchies of ODEs, are a topic of great current interest. Here we give an improved method of constructing BTs for hierarchies of ODEs. This approach is then applied to fourth Painlevé (PIV ) hierarchies recently found by the same authors [Publ. Res. Inst. Math. Sci. (Kyoto) 37 327–347 (2001)]. We ...
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For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schrödinger equation) a general procedure for constructing Bäcklund transformation is proposed. The corresponding BT is shown to preserve the Poisson bracket. The proof is given by a direct calculation using the r-matrix expression for the Poisson bracket.
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This is the second part of the paper devoted to the general proof of canon-icity of Bäcklund transformation (BT) for a Hamiltonian integrable system governed by SL(2)-invariant r-matrix. Introducing an extended phase space from which the original one is obtained by imposing a 1st kind constraint, we are able to prove the canonicity of BT in a new way. The new proof allows to explain naturally t...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2017
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/aa59c9