We obtain 3 × 3 matrix Lax pairs for systems of ODEs that are solvable in terms of the fourth, fifth and sixth Painlevé equations by considering similarity reductions of the scattering Lax pair for the (2+1)-dimensional three-wave resonant interaction system. These results allow us to construct new 3× 3 Lax representations for the fourth and fifth Painlevé equations, together with the previousl...

— Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense,...

We study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov equation, and their matrix Lax representations defined by local Yang--Baxter equation. Sergeev [S.M. 1998 Lett. Math. Phys. 45, 113--119] presented classification results on three-dimensional maps obtained from equation for a certain class of matrix-functions in situation when possesses unique solution determine...

We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when f : X → Y is a semi-algebraic map and ...

This study aimed to determine whether absolute sex hormone concentrations predict the magnitude of knee joint laxity changes across the menstrual cycle. Twenty-two females (18-30 years, body mass index <or=30), who reported normal menstrual cycles for the previous 6 months were tested daily across one complete menstrual cycle for serum levels of estradiol (E=pg/mL), progesterone (P=ng/mL), and ...

We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative Bäcklund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model. PACS...

We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Mong...