On non commutative sinh-Gordon Equation

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.Comment: 7 Page

Noncommutative Deformation of Spinor Zero Mode and ADHM Construction

A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative R^4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative R^4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative R^4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions added,typos correcte

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

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

Molecular Dynamics Simulation of Heat-Conducting Near-Critical Fluids

Using molecular dynamics simulations, we study supercritical fluids near the gas-liquid critical point under heat flow in two dimensions. We calculate the steady-state temperature and density profiles. The resultant thermal conductivity exhibits critical singularity in agreement with the mode-coupling theory in two dimensions. We also calculate distributions of the momentum and heat fluxes at fixed density. They indicate that liquid-like (entropy-poor) clusters move toward the warmer boundary and gas-like (entropy-rich) regions move toward the cooler boundary in a temperature gradient. This counterflow results in critical enhancement of the thermal conductivity

Lost equivalence of nonlinear sigma and CP1CP^{1} models on noncommutative space

We show that the equivalence of nonlinear sigma and $CP^{1}$ 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

Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

Conserved Quantities in Noncommutative Principal Chiral Model with Wess-Zumino Term

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin {\it et.al} \cite{BIZZ}. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zeroth- and first-order equations of motion, zero-curvature condition, iteration method, Lax formalism, local and non-local conserved quantities.Comment: 14 Page

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.

On Non-Commutative Integrable Burgers Equations

We construct the recursion operators for the non-commutative Burgers equations using their Lax operators. We investigate the existence of any integrable mixed version of left- and right-handed Burgers equations on higher symmetry grounds.Comment: 8 page