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101.
This paper carries out the integration of the coupled KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The domain restrictions of the coefficients of nonlinear and dispersion terms fall out. The results are then supplemented by numerical simulations. 相似文献
102.
Indranil Biswas 《Transactions of the American Mathematical Society》2002,354(10):3883-3891
Let be an ample line bundle over a complex abelian variety . We show that the space of all global sections over of and are both of dimension one. Using this it is shown that the moduli space of rank one holomorphic connections on a compact Riemann surface does not admit any nonconstant algebraic function. On the other hand, is biholomorphic to the moduli space of characters of , which is an affine variety. So is algebraically distinct from the character variety if is of genus at least one.
103.
Let X be a connected Riemann surface equipped with a projective structure
. Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using
, this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using
, a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed. 相似文献
104.
A. Biswas D. Milovic 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):155
Recent developments in the study of nonlinear phenomena have led to the realization that a combination of the concepts of
integrability, geometry and topology provides a new powerful framework for describing a great variety of physical systems.
It was therefore felt that the compilation of a special issue comprising articles on the interdiseiplinary topic of Geometry,
Integrability and Nonlinearity in Condensed Matter Physics, would indeed be timely. The enthusiastic response and support
that we received from the active researchers in this subject, when we organized an International Conference on the above topic
from July 15 to July 20, 2001, in Bansko, Bulgaria, provided a further motivation for undertaking this task.
As the topic is interdisciplinary in nature, the articles in this volume contain new results on a wide range of subjects.
These include among others, integrable equations and the interplay between geometry and nonlinearity, the role of optical
solitons in communication. (and, possibly, computation), common nonlinear and geometrical aspects of condensed matter, field
theory, and so on. The increasingly important role played by geometry and topology in diverse areas such as the quantum Hall
effect, localization, deformation and elasticity, quasiparticle kinetics and dynamics, spin systems, membranes, is highlighted
in some of the articles. There are papers in which essential links of nonlinearity to differential geometry are identified
and many elegant mathematical methods are presented. Some other articles focus on how the mathematical tools of geometry and
nonlinear analysis can be applied to solve certain physical problems.
Given the vast range of titles, it was difficult to strictly divide the contributions into distinct categories. Except for
the pedagogical introductory article by Rajaraman titled "CP
N
Solitons in Quantum Hall Systems", which essentially "sets the stage" for the various themes covered, we have grouped the
articles broadly under the following headings: Geometry, integrability and mathematical physics; Solitons: Interaction phenomena,
nonlinear optics; Condensed matter physics; Soft condensed matter physics; Quantum phenomena.
We gratefully acknowledge the support from Los Alamos National Lab, USA; Université de Cergy-Pontoise, France; The Abdus Salam
International Centre for Theoretical Physics, Trieste, Italy and the Institute for Nuclear Research and Nuclear Energy, Sofia,
Bulgaria, in putting this special volume together. We believe that the cross-fertilization and synergy of a host of ideas
in seemingly disparate fields of physics would lead to the natural emergence of new paradigms, which in turn could pave the
way for collaborative research to arrive at new solutions of complex nonlinear problems. It is our hope that this topical
issue will be useful in providing an impetus for achieving this broad objective.
Radha Balakrishnan, Chennai, India
Rossen Dandoloff, Cergy-Pontoise, France
Vladimir Gerdjikov, Sofia, Bulgaria
Dimitar Pushkarov, Sofia, Bulgaria
Avadh Saxena, Los Alamos, USA 相似文献
105.
106.
107.
Let M be an irreducible projective variety, over an algebraically closed field k of characteristic zero, equipped with an action of a connected algebraic group S over k. Let E
G
be a principal G-bundle over M equipped with a lift of the action of S on M, where G is a connected reductive linear algebraic group. Assume that E
G
admits a reduction of structure group to a maximal torus TG. We give a necessary and sufficient condition for the existence of a T-reduction of E
G
which is left invariant by the action of S on E
G
. 相似文献
108.
P. Paasche C. Angelescu S. Ananthamurthy D. Biswas T. Valenzuela G. Werth 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,22(2):183-188
We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried
out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the
same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit.
The characteristic frequencies at which these instabilities occur, obey a relation that is given by n
zω
z + n
+ω
+ + n
-ω
- = 0, where ω
z, ω
+ and ω
- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential.
Received 5 August 2002 / Received in final form 14 October 2002 Published online 17 December 2002
RID="a"
ID="a"Present address: Dept. of Physics, Rampurhat College, Rampurhat, Birbhum, West Bengal, India.
RID="b"
ID="b"e-mail: werth@mail.uni-mainz.de 相似文献
109.
Let X be a Riemann surface equipped with a projective structure. Let
be a square-root of the holomorphic cotangent bundle K
X
. Consider the symplectic form on the complement of the zero section of
obtained by pulling back the symplectic form on K
X
using the map 2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K
X
equipped with the natural symplectic form. 相似文献
110.
Anjan Biswas Swapan Konar Essaid Zerrad 《International Journal of Theoretical Physics》2007,46(1):157-169
The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of
quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers
along with filters. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived.
The numerical simulations support the quasi-particle theory.
OCIS codes: 060.2310; 060.4510; 060.5530; 190.3270; 190.4370. 相似文献