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...

Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often composed of a large number of interconnected and interacting entities exhibiting much richer global scal...

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...

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-...

The (2+1)-dimensional higher-order Broer-Kaup (HBK) system is studied by nonlocal symmetry method and consistent tanh expansion (CTE) method in this paper. Some exact interaction solutions among different nonlinear excitations such as solitons, rational waves, periodic waves and corresponding images are explicitly given. PACS numbers: 02.30.Jr, 11.10.Lm, 02.20.-a, 04.20.Jb

A complete set of conditions describing the transition across the dissipationless undular bore (dispersive shock) is derived for nonlinear weakly dispersive conservative systems that generally are not integrable by the inverse spectral transform method. In the absence of integrable structure, we postulate modulation description of the undular bore with the aid of the averaged Whitham equations ...

In this work we estimate the radius and the mass of a self-gravitating system made of axions. The quantum axion field satisfies the Klein-Gordon equation in a curved space-time and the metric components of this space-time are solutions to the Einstein equations with a source term given by the vacuum expectation value of the energy-momentum operator constructed from the axion field. As a first s...