We introduce certain Backlund transformations for rational solutions of the Painleve VI equation. These act on a family tau functions. They are obtained from reducing Hirota bilinear equations that describe relation between points in 3 component polynomial KP Grassmannian. In this way we obtain root lattice A5. also show A5 can be related to F4(1) lattice. thus relate functions, parametrized by...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

Radial solutions to the elliptic sinh-Gordon and Tzitzeica equations can be interpreted as Abelian vortices on certain surfaces of revolution. These have a conical excess angle at infinity (in way which makes them similar Elizabethan ruff collars). While they not embedded in Euclidean 3-space, we will show that globally hyperbolic space. The existence these embeddings follows from asymptotic an...

We show that the local magnetization in the massive boundary Ising model on the half-plane with boundary magnetic field satisfies second order linear differential equation whose coefficients are expressed through Painleve function of the III kind.

A classical question in surface theory is which data are sufficient to describe a surface in space up to rigid motions. Bonnet suggested that mean curvature and metric should suffice to determine the surface generically. The local theory was developed by Bonnet [6], Cartan [4] and Chern [5] who showed the existence of various 1-parameter families of Bonnet surfaces, i.e., surfaces with the same...

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painleve equation. One obtains a Riemann–Hilbert correspondence between moduli spaces rank two connections on ℙ1 and for monodromy data. these identified with Okamoto–Painleve varieties property follows. For an explicit computation full group Backlund transformations, three introduced, inspired by symmetric form PIV, studied M. Noumi...

We present a new method for the derivation of mappings HKY type. These are second-order which do not have biquadratic invariant like QRT mappings, but rather an degree higher than two in at least one variables. Our is based on folding transformations exist some discrete Painleve equations. They relate variable equation to square other one. By considering autonomous limit these relations we deri...