ar X iv : s ol v - in t / 9 90 90 27 v 1 2 6 Se p 19 99 On two aspects of the Painlevé analysis
نویسنده
چکیده
The Calogero equation is used to illustrate the following two aspects of the Painlevé analysis of PDEs: (i) the singular expansions of solutions around characteristic hypersurfaces are neither single-valued functions of independent variables nor single-valued functionals of data; (ii) the truncated singular expansions not necessarily lead to the simplest, elementary, Bäcklund autotransformation related to the Lax pair.
منابع مشابه
ar X iv : s ol v - in t / 9 90 90 16 v 1 1 6 Se p 19 99 Darboux Transformation and Supersymmetric KP Hierarchy
We construct Darboux transformations for the supersymmetric KP hierarchy. We show that the naive candidate does not work due to the pressure of the odd flows,but its composition does give rise to a meaningful Darboux transformation. We also consider the b inary Darboux transformation for the hierarchy. The iterations of both type of Darboux transformations are briefly discussed.
متن کاملar X iv : s ol v - in t / 9 90 70 08 v 2 2 9 Se p 19 99 Inter - relationships between orthogonal , unitary and symplectic matrix ensembles
We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding orthogonal ensemble form a symplectic ensemble, and similarly classify those weights for which alternate eigenvalues from a union of two orthogonal ensembles forms ...
متن کاملar X iv : s ol v - in t / 9 50 90 03 v 3 1 2 Se p 19 95 Proofs of Two Conjectures Related to the Thermodynamic Bethe
We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel e −(u(θ)+u(θ)) cosh θ−θ ′ 2 .
متن کاملar X iv : s ol v - in t / 9 90 90 22 v 1 2 1 Se p 19 99 SELF - SIMILARITY IN SPECTRAL PROBLEMS AND q - SPECIAL FUNCTIONS 1
Similarity symmetries of the factorization chains for one-dimensional differential and finite-difference Schrödinger equations are discussed. Properties of the potentials defined by self-similar reductions of these chains are reviewed. In particular, their algebraic structure, relations to q-special functions, infinite soliton systems, supersymmetry, coherent states, orthogonal polynomials, one...
متن کاملar X iv : m at h - ph / 9 90 90 25 v 1 2 1 Se p 19 99 The symmetries of the Manton superconductivity model
The symmetries and conserved quantities of Manton's modified superconductiv-ity model with non-relativistic Maxwell-Chern-Simons dynamics (also related to the Quan-tized Hall Effect) are obtained in the " Kaluza-Klein type " framework of Duval et al. 1. Introduction Recently [1], Manton proposed a modified version of the Landau-Ginzburg theory of superconductivity. His equations, defined on (2 ...
متن کامل