In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring link between different algebraic (in terms double Poisson algebras and vertex algebras) geometric bivectors) definitions. We introduce multiplicative (PVAs) as suitable noncommutative counterpart to PVAs, used describe equations in commutative setting, prove that thes...

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...

4 KARL-HEINZ GARTEMANN, BIRTE ABT, THOMAS BEKEL, ANNETTE BURGER, 5 JUTTA ENGEMANN, MONIKA FLÜGEL, 1 LARS GAIGALAT, ALEXANDER 6 GOESMANN, INES GRÄFEN, JÖRN KALINOWSKI, OLAF KAUP, OLIVER 7 KIRCHNER, LUTZ KRAUSE, BURKHARD LINKE, ALICE McHARDY, FOLKER 8 MEYER,‡ SANDRA POHLE, CHRISTIAN RÜCKERT, 2,3 SUSANNE SCHNEIKER, EVA9 MARIA ZELLERMANN, ALFRED PÜHLER, RUDOLF EICHENLAUB,* OLAF 10 KAISER, AND DANIE...

The main purpose of this research is to propose a new methodology observe class time-fractional generalized fifth-order Korteweg–de Vries equations. Laplace transform along with homotopy perturbation algorithm utilized for the solution and analysis in current study. This extended technique provides improved convergent series solutions through symbolic computation. proposed applied Sawada–Kotera...

The cubic nonlinear Schroedinger equation (NLS) describes the space-time evolution of narrow-banded wave trains in one space and one time (1 + 1) dimensions. The richness of nonlinear wave motions described by NLS is exemplified by the fully nonlinear envelope soliton and “breather” solutions, which are fully understood only in terms of the general solution of the equation as described by the i...

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...

For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...

Late distributive disambiguation, (3), increases reading measures (first pass, total times, regressions) compared to late collective disambiguation, (4). Early distributive disambiguation, (1), does not significantly increase reading measures compared to early collective disambiguation, (2). Interpretation: Potentially ambiguous predicates are interpreted collectively by the processor ⇒ garden-...