Relativistic DNLS and Kaup-Newell Hierarchy

By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit $c \rightarrow \infty$ it reduces to DNLS equation and preserves integrability at any order of relativistic corrections. The compact explicit representation of the linear problem for this equation becomes possible due to notions of the $q$-calculus with two bases, one of which is the recursion operator, and another one is the spectral parameter

Self-Dual Vortices in Chern-Simons Hydrodynamics

The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schr\"odinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\hbar^2$) deformed strength of quantum potential the model is gauge equivalent to the standard Schr\"odinger equation with Planck constant $\hbar$, while for the strength (1 + $\hbar^2$), to the pair of diffusion-anti-diffusion equations. Specifying the gauge field as Abelian Chern-Simons (CS) one in 2+1 dimensions interacting with the Nonlinear Schr\"odinger field (the Jackiw-Pi model), we represent the theory as a planar Madelung fluid, where the Chern-Simons Gauss law has simple physical meaning of creation the local vorticity for the fluid flow. For the static flow, when velocity of the center-of-mass motion (the classical velocity) is equal to the quantum one (generated by quantum potential velocity of the internal motion), the fluid admits N-vortex solution. Applying the Auberson-Sabatier type gauge transform to phase of the vortex wave function we show that deformation parameter $\hbar$, the CS coupling constant and the quantum potential strength are quantized. Reductions of the model to 1+1 dimensions, leading to modified NLS and DNLS equations with resonance soliton interactions are discussed.Comment: 12 pages, Tex, to be published in Proc. "NEEDS'2000", Gokova, Turkey, 2000; Theor. and Math.Physic

Chiral Resonant Solitons in Broer-Kaup Type New Hydrodynamic Systems

New Broer-Kaup type systems of hydrodynamic equations are derived from the derivative reaction-diffusion systems arising in SL(2,R) Kaup-Newell hierarchy, represented in the non-Madelung hydrodynamic form. A relation with the problem of chiral solitons in quantum potential as a dimensional reduction of 2+1 dimensional Chern-Simons theory for anyons is shown. By the Hirota bilinear method, soliton solutions are constructed and the resonant character of soliton interaction is found.Comment: 16 pages, 2 figure

Soliton resonances in a generalized nonlinear Schrödinger equation

It is shown that a generalized nonlinear Schrödinger equation proposed by Malomed and Stenflo admits, for a specific range of parameters, resonant soliton interaction. The equation is transformed to the 'resonant' nonlinear Schrödinger equation, as originally introduced to describe black holes in a Madelung fluid and recently derived in the context of uniaxial wave propagation in a cold collisionless plasma. A Hirota bilinear representation is obtained and soliton solutions are thereby derived. The one-soliton solution interpretation in terms of a black hole in two-dimensional spacetime is given. For the two-soliton solution, resonant interactions of several kinds are found. The addition of a quantum potential term is considered and the reduction is obtained to the resonant NLS equation. © 2008 IOP Publishing Ltd.Izmir Institute of Technology, Turkey, Grant BAP 25 200

Resonance NLS Solitons as Black Holes in Madelung Fluid

A new resonance version of NLS equation is found and embedded to the reaction-diffusion system, equivalent to the anti-de Sitter valued Heisenberg model, realizing a particular gauge fixing condition of the Jackiw-Teitelboim gravity. The space-time points where dispersion change the sign correspond to the event horizon, and the soliton solutions to the AdS black holes. The soliton with velocity bounded above describes evolution on the hyperboloid with nontrivial winding number and create under collisions the resonance states with a specific life time.Comment: Plain Tex, 12 pages, 6 figure

Microstructure and Corrosion Behavior of Ni-Alloy/CrN Nanolayered Coatings

The Ni-alloy/CrN nanolayered coatings, Ni-Al/CrN and Ni-P/CrN, were deposited on (100) silicon wafer and AISI 420 stainless steel substrates by dual-gun sputtering technique. The influences of the layer microstructure on corrosion behavior of the nanolayered thin films were investigated. The bilayer thickness was controlled approximately 10 nm with a total coating thickness of 1m. The single-layer Ni-alloy and CrN coatings deposited at 350∘C were also evaluated for comparison. Through phase identification, phases of Ni-P and Ni-Al compounds were observed in the single Ni-alloy layers. On the other hand, the nanolayered Ni-P/CrN and Ni-Al/CrN coatings showed an amorphous/nanocrystalline microstructure. The precipitation of Ni-Al and Ni-P intermetallic compounds was suppressed by the nanolayered configuration of Ni-alloy/CrN coatings. Through Tafel analysis, the corr and corr values ranged from –0.64 to –0.33 V and 1.42×10−5 to 1.14×10−6 A/cm2, respectively, were deduced for various coating assemblies. The corrosion mechanisms and related behaviors of the coatings were compared. The coatings with a nanolayered Ni-alloy/CrN configuration exhibited a superior corrosion resistance to single-layer alloy or nitride coatings

Surface Electron-Hole Rich Species Active in the Electrocatalytic Water Oxidation.

Iridium and ruthenium and their oxides/hydroxides are the best candidates for the oxygen evolution reaction under harsh acidic conditions owing to the low overpotentials observed for Ru- and Ir-based anodes and the high corrosion resistance of Ir-oxides. Herein, by means of cutting edge operando surface and bulk sensitive X-ray spectroscopy techniques, specifically designed electrode nanofabrication and ab initio DFT calculations, we were able to reveal the electronic structure of the active IrOx centers (i.e., oxidation state) during electrocatalytic oxidation of water in the surface and bulk of high-performance Ir-based catalysts. We found the oxygen evolution reaction is controlled by the formation of empty Ir 5d states in the surface ascribed to the formation of formally IrV species leading to the appearance of electron-deficient oxygen species bound to single iridium atoms (μ1-O and μ1-OH) that are responsible for water activation and oxidation. Oxygen bound to three iridium centers (μ3-O) remains the dominant species in the bulk but do not participate directly in the electrocatalytic reaction, suggesting bulk oxidation is limited. In addition a high coverage of a μ1-OO (peroxo) species during the OER is excluded. Moreover, we provide the first photoelectron spectroscopic evidence in bulk electrolyte that the higher surface-to-bulk ratio in thinner electrodes enhances the material usage involving the precipitation of a significant part of the electrode surface and near-surface active species

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a B\"acklund transformation.Comment: 13 page