On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the $\big(\frac{G'}{G}\big)$ expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained.Comment: Accepted for Publication in Commun. Nonlin. Sci. Num. Sim. (2012

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schr\"{o}dinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.Comment: Accepted for publication in The European Physical Journal

Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates

We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter that present in the similarity transformation should satisfy a constraint for the considered equation to be integrable and yield the desired solutions. We consider two different forms of functional parameters and investigate how the density of the rogue wave and breather profiles vary with respect to these functional parameters. We also construct vector localized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate system. We then investigate how the vector localized density profiles modify in the constant density background with respect to the functional parameters. Our results may help to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einstein condensate systems.Comment: 16 pages, Published in Eur. Phys. J.

Short-wavelength secondary instabilities in homogeneous and stably stratified shear flows

We present a numerical investigation of three-dimensional, short-wavelength linear instabilities in Kelvin-Helmholtz (KH) vortices in homogeneous and stratified environments. The base flow, generated using two-dimensional numerical simulations, is characterized by the Reynolds number and the Richardson number defined based on the initial one-dimensional velocity and buoyancy profiles. The local stability equations are then solved on closed streamlines in the vortical base flow, which is assumed quasi-steady. For the unstratified case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case, the early time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability strongly influenced by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of instability (convective branch) that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability branches appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with results from global instability studies for both homogeneous and stratified cases. Compartmentalized analyses are then used to elucidate the role of shear and stratification on the identified instabilities. The role of buoyancy is shown to be critical after the primary KH instability saturates, with the dominant convective instability shown to occur in regions with the strongest statically unstable layering. We conclude by highlighting the potentially insightful role that the local approach may offer in understanding the secondary instabilities in other flows.Comment: Submitted to J. Fluid Mech., 20 pages, 10 figure

Identification of Allelochemicals from Terminalia Chebula

This study was an experiental research to identify the chemicals contained in terminalia chebula.The dried leaves and barks were ground to a fine powder in a Wiley Mill (40 mesh), using this powder for aqueous extract prepared by the method of Heisey (1990). Bioassay studies were also carried out following the method of Heisey (1990). The extraction of phenolic compounds for GC analysis was carried out by the method of Kil and Yum (1983). The comparison of the leaf and bark extracts was done. The result of our study showed that the leaf extracts of the T.chebula contains more quantity of hydroquinone, trans-cinnamic acid, gentisic acid, vanillic acid, syringic acid and transferulic acid (phnolic acids) otherwise known as allochemicals than the bark and were more inhibitory to seeding growth of Cassia occidentals and Crotalaria retusa than the bark extracts in bioassay studies. The implication is that Terminalia Chebula will be extremely useful in future to control the weed growth in agroecosystem. Keywords: Terminnlia chebula, Cassia occidentals, Crotalaria retusa and allelo chemicals.African Research Review Vol. 2 (3) 2008: pp. 306-31