619 research outputs found
Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations
We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
On a direct approach to quasideterminant solutions of a noncommutative KP equation
A noncommutative version of the KP equation and two families of its solutions
expressed as quasideterminants are discussed. The origin of these solutions is
explained by means of Darboux and binary Darboux transformations. Additionally,
it is shown that these solutions may also be verified directly. This approach
is reminiscent of the wronskian technique used for the Hirota bilinear form of
the regular, commutative KP equation but, in the noncommutative case, no
bilinearising transformation is available.Comment: 11 page
Transitions among crystal, glass, and liquid in a binary mixture with changing particle size ratio and temperature
Using molecular dynamics simulation we examine changeovers among crystal,
glass, and liquid at high density in a two dimensional binary mixture. We
change the ratio between the diameters of the two components and the
temperature. The transitions from crystal to glass or liquid occur with
proliferation of defects. We visualize the defects in terms of a disorder
variable "D_j(t)" representing a deviation from the hexagonal order for
particle j. The defect structures are heterogeneous and are particularly
extended in polycrystal states. They look similar at the crystal-glass
crossover and at the melting. Taking the average of "D_j(t)" over the
particles, we define a disorder parameter "D(t)", which conveniently measures
the degree of overall disorder. Its relaxation after quenching becomes slow at
low temperature in the presence of size dispersity. Its steady state average is
small in crystal and large in glass and liquid.Comment: 7 pages, 10 figure
B\"acklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
We present Backlund transformations for the noncommutative anti-self-dual
Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a
series of exact solutions from a simple seed solution. The solutions generated
by this approach are represented in terms of quasideterminants. We also explain
the origins of all of the ingredients of the Backlund transformations within
the framework of noncommutative twistor theory. In particular we show that the
generated solutions belong to a noncommutative version of the Atiyah-Ward
ansatz.Comment: v2: 21 pages, published versio
Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation
Matrix solutions of a noncommutative KP and a noncommutative mKP equation
which can be expressed as quasideterminants are discussed. In particular, we
investigate interaction properties of two-soliton solutions.Comment: 2 figure
Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space
We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons
gauge theory coupled to a nonrelativistic complex adjoint matter on
noncommutative space. Soliton configurations of this model are related the
solutions of the chiral model on noncommutative plane. A generalized
Uhlenbeck's uniton method for the chiral model on noncommutative space provides
explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory
are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n'
should be an integer upon quantization. Toda and Liouville models are
generalized to noncommutative plane and the solutions are provided by the
uniton method. We also define affine Toda and sine-Gordon models on
noncommutative plane. Finally the first order moduli space dynamics of
Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur
New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model
Investigating the solitons in the non-commutative model, we have
found a new set of BPS solitons which does not have counterparts in the
commutative model.Comment: 8 pages, LaTeX2e, references added, improvements to discussions,
Version to be published in JHE
Lost equivalence of nonlinear sigma and models on noncommutative space
We show that the equivalence of nonlinear sigma and models which is
valid on the commutative space is broken on the noncommutative space. This
conclusion is arrived at through investigation of new BPS solitons that do not
exist in the commutative limit.Comment: 17 pages, LaTeX2
Noncommutative Burgers Equation
We present a noncommutative version of the Burgers equation which possesses
the Lax representation and discuss the integrability in detail. We find a
noncommutative version of the Cole-Hopf transformation and succeed in the
linearization of it. The linearized equation is the (noncommutative) diffusion
equation and exactly solved. We also discuss the properties of some exact
solutions. The result shows that the noncommutative Burgers equation is
completely integrable even though it contains infinite number of time
derivatives. Furthermore, we derive the noncommutative Burgers equation from
the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is
an evidence for the noncommutative Ward conjecture. Finally, we present a
noncommutative version of the Burgers hierarchy by both the Lax-pair generating
technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato
theory and the integrability added, references added, version to appear in J.
Phys.
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