7,550 research outputs found
Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies
In this paper, we give a procedure of how to discretize the recursion
operators by considering unified bilinear forms of integrable hierarchies. As
two illustrative examples, the unified bilinear forms of the AKNS hierarchy and
the KdV hierarchy are presented from their recursion operators. Via the
compatibility between soliton equations and their auto-B\"acklund
transformations, the bilinear integrable hierarchies are discretized and the
discrete recursion operators are obtained. The discrete recursion operators
converge to the original continuous forms after a standard limit.Comment: 11Page
Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
A previously proposed variational approach for momentum-conserving systems
[J. Liu et.al., Phys. Rev. E 91, 042910 (2015)] is extended to systematically
investigate general momentum-nonconserving nonlinear lattices. Two intrinsic
identities characterizing optimal reference systems are revealed, which enables
us to derive explicit expressions for optimal variational parameters. The
resulting optimal harmonic reference systems provide information for the band
gap as well as the dispersion of renormalized phonons in nonlinear lattices. As
a demonstration, we consider the one-dimensional \phi^?4 lattice. By combining
the transfer integral operator method, we show that the phonon band gap endows
a simple power-law temperature dependence in the weak stochasticity regime
where predicted dispersion is reliable by comparing with numerical results. In
addition, an exact relation between ensemble averages of the \phi^?4 lattice in
the whole temperature range is found, regardless of the existence of the strong
stochasticity threshold.Comment: 8 pages, 3 figure
Wave turbulence in Bose-Einstein condensates
The kinetics of nonequilibrium Bose-Einstein condensates are considered
within the framework of the Gross-Pitaevskii equation. A systematic derivation
is given for weak small-scale perturbations of a steady confined condensate
state. This approach combines a wavepacket WKB description with the weak
turbulence theory. The WKB theory derived in this paper describes the effect of
the condensate on the short-wave excitations which appears to be different from
a simple renormalization of the confining potential suggested in previous
literature.Comment: 33 pages 2 figure
Analytic Non-integrability in String Theory
Using analytic techniques developed for Hamiltonian dynamical systems we show
that a certain classical string configurations in AdS_5 x X_5 with X_5 in a
large class of Einstein spaces, is non-integrable. This answers the question of
integrability of string on such backgrounds in the negative. We consider a
string localized in the center of AdS_5 that winds around two circles in the
manifold X_5.Comment: 14 page
Unreduced Dynamic Complexity: Towards the Unified Science of Intelligent Communication Networks and Software
Operation of autonomic communication networks with complicated user-oriented functions should be described as unreduced many-body interaction process. The latter gives rise to complex-dynamic behaviour including fractally structured hierarchy of chaotically changing realisations. We recall the main results of the universal science of complexity (http://cogprints.org/4471/) based on the unreduced interaction problem solution and its application to various real systems, from nanobiosystems (http://cogprints.org/4527/) and quantum devices to intelligent networks (http://cogprints.org/4114/) and emerging consciousness (http://cogprints.org/3857/). We concentrate then on applications to autonomic communication leading to fundamentally substantiated, exact science of intelligent communication and software. It aims at unification of the whole diversity of complex information system behaviour, similar to the conventional, "Newtonian" science order for sequential, regular models of system dynamics. Basic principles and first applications of the unified science of complex-dynamic communication networks and software are outlined to demonstrate its advantages and emerging practical perspectives
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