We construct a new variety of N = 2 supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for a = 4, N = 2 KdV and multi-component N = 2 NLS hierarchies. As an important particular case, we obtain Lax operator for N = 4 super KdV system. A similar extension of one of N = 2 super Boussinesq hierarchies is given. We also present a minimal N = 4 supersymmetr...

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian ...

A typical and effective way to construct a higher dimensional integrable equation is to extend the Lax pair for a (1 + 1) dimensional equation known as integrable to higher dimensions. Here we construct an alternative modified KdV equation in (2+1) dimensions by the higherdimensional extension of a Lax pair. And it is shown that this higher dimensional modified KdV equation passes the Painlevé ...

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin et.al [17]. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zerothand first-order equations of motion, zero-curv...

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian ...

We discuss the use of relation lifting in the theory of set-based coalgebra and coalgebraic logic. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavioral equivalence. On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullb...

The characterization of stably closed maps of topological spaces as the closed maps with compact fibres and the role of the Kuratowski-Mrówka’ Theorem in this characterization are being explored in the general context of lax (T, V )-algebras, for a quantale V and a Setmonad T with a lax extension to V -relations. The general results are being applied in standard (topological and metric) and non...

Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.

A partial nonlinear extension of Lax-Richtmyer approximation theory by Aradhana Kumari Adviser: Professor Dennis Sullivan Lax and Richtmyer developed a theory of algorithms for linear initial value problems that guarantees, under certain circumstances, the convergence to numerical solution of initial value problem. The assumptions are first that the difference equations (algorithms) approximate...