Lie symmetries, Kac-Moody-Virasoro algebras and integrability of certain (2+1)-dimensional nonlinear evolution equations

In this paper we study Lie symmetries, Kac-Moody-Virasoro algebras, similarity reductions and particular solutions of two different recently introduced (2+1)-dimensional nonlinear evolution equations, namely (i) (2+1)-dimensional breaking soliton equation and (ii) (2+1)-dimensional nonlinear Schr\"odinger type equation introduced by Zakharov and studied later by Strachan. Interestingly our studies show that not all integrable higher dimensional systems admit Kac-Moody-Virasoro type sub-algebras. Particularly the two integrable systems mentioned above do not admit Virasoro type subalgebras, eventhough the other integrable higher dimensional systems do admit such algebras which we have also reviewed in the Appendix. Further, we bring out physically interesting solutions for special choices of the symmetry parameters in both the systems

Analysis of 83mKr prompt scintillation signals in the PIXeY detector

Prompt scintillation signals from 83mKr calibration sources are a useful metric to calibrate the spatial variation of light collection efficiency and electric field magnitude of a two phase liquid-gas xenon time projection chamber. Because 83mKr decays in two steps, there are two prompt scintillation pulses for each calibration event, denoted S1a and S1b. We study the ratio of S1b to S1a signal sizes in the Particle Identification in Xenon at Yale (PIXeY) experiment and its dependence on the time separation between the two signals (Δ t), notably its increase at low Δ t. In PIXeY data, the Δ t dependence of S1b/S1a is observed to exhibit two exponential components: one with a time constant of 0.05 ± 0.02 μ s, which can be attributed to processing effects and pulse overlap and one with a time constant of 10.2 ± 2.2 μs that increases in amplitude with electric drift field, the origin of which is not yet understood

A symmetry classification for a class of (2+1)-nonlinear wave equation

In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $(2+1)$-nonlinear wave equation

A note on the Painleve analysis of a (2+1) dimensional Camassa-Holm equation

We investigate the Painleve analysis for a (2+1) dimensional Camassa-Holm equation. Our results show that it admits only weak Painleve expansions. This then confirms the limitations of the Painleve test as a test for complete integrability when applied to non-semilinear partial differential equations.Comment: Chaos, Solitons and Fractals (Accepted for publication

Electro oxidation of Malachite Green and Modeling Using ANN

This study involves the electro-oxidation of malachite green, a triphenyl methane dye, extensively used in industries and aquaculture, and later banned in most developed countries because of its potential carcinogenicity, mutagenicity and teratogenicity in mammals. The study is conducted in a batch electro-chemical reactor using the catalytic anode (made of noble oxide coated, RuOx-TiOx, titanium expanded mesh) that mediates the oxidation of organic species by the formation of higher oxidation state oxides of the metal (e.g., RuO2 or IrO2). The operating variables are current density, electrolysis time and initial dye concentration. Complete removal of the dye has been reported by 41 minutes of treatment at a current density of 2.2 A dm–2 for the case of initial dye concentration of 200 mg L–1. The experimental data are modeled using back-propagation artificial neural network. The results were compared with experimental observations, and found that the model predictions adequately match experimental observations. Combination of the factors giving complete removal of the dye has also been commented