Using the two-dimensional nonlinear Schrödinger equation as a model example, we present general method for recovering nonlinearity of dispersive from its small-data scattering behavior. We prove that under very mild assumptions on nonlinearity, wave operator uniquely determines does map. Evaluating map well-chosen initial data, reduce problem to an inverse convolution problem, which solve by me...

It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quadgraphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff.

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

Abstract The pentagram map, introduced by Schwartz [The map. Exp. Math. 1 (1) (1992), 71–81], is a dynamical system on the moduli space of polygons in projective plane. Its real and complex dynamics have been explored detail. We study map over an arbitrary algebraically closed field characteristic not equal to 2. prove that twisted discrete integrable system, sense algebraic complete integrabil...

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...

A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N = 2 super Wn algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulted hierarchy contains the N = 2 super Virasoro algebra as a proper subalgebra. The simplest cases are discussed in detail. In particular, it is proved that the supersymm...

In [CY98] Crane and Yetter introduced a deformation theory for monoidal categories. The related deformation theory for monoidal functors introduced by Yetter in [Yet98] is a proper generalization of Gerstenhaber’s deformation theory for associative algebras [Ger63, Ger64, GS88]. In the present paper we solidify the analogy between lax monoidal functors and associative algebras by showing that u...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

We examine the conformal preperty of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturally gives a family of nonlocal extended conformal algebras. We give two examples of such algebras and find that they are similar to Bilal's V algebra. By taking a gauge transformation one can map the constrained KP hierarchy to Kupershmidt's nonst...

We investigate those lax extensions of a Set-monad T = (T,m, e) to the category V-Rel of sets and V-valued relations for a quantale V = (V,⊗, k) that are fully determined by maps ξ : TV → V . We pay special attention to those maps ξ that make V a T-algebra and, in fact, (V,⊗, k) a monoid in the category SetT with its cartesian structure. Any such map ξ forms the main ingredient to Hofmann’s not...