Applied and Industrial Mathematics Research Group

Canberra, Australia

Applied and Industrial Mathematics Research Group

Canberra, Australia

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Bhrawy A.H.,King Abdulaziz University | Bhrawy A.H.,Beni Suef University | Alshaery A.A.,King Abdulaziz University | Hilal E.M.,King Abdulaziz University | And 4 more authors.
Optik | Year: 2014

This paper studies coupled nonlinear Schrödinger's equation (NLSE) that appears in a cascaded system. Both Kerr law and power law nonlinearities are considered. Bright and dark soliton solutions are retrieved for these nonlinearities. The corresponding constraint conditions naturally fall out that from the mathematical expressions that must remain valid for solitons to exist. © 2014 Elsevier GmbH. All rights reserved.


Bhrawy A.H.,King Abdulaziz University | Bhrawy A.H.,Beni Suef University | Alshaery A.A.,King Abdulaziz University | Hilal E.M.,King Abdulaziz University | And 8 more authors.
Optik | Year: 2014

This paper studies the propagation of solitons through birefringent fibers in the presence of spatio-temporal dispersion. Both Kerr and parabolic laws of nonlinearity are addressed. The exact 1-soliton solutions are obtained. There are several constraint conditions that ensure soliton solutions are derived. Three types of solitons are obtained: bright, dark and singular solitons. © 2014 Elsevier GmbH.


Fromm M.D.,U.S. Navy | McRae R.H.D.,ACT Emergency Services Agency | Sharples J.J.,Applied and Industrial Mathematics Research Group | Kablick III G.P.,U.S. Navy
Australian Meteorological and Oceanographic Journal | Year: 2012

On 22 November 2006 a pair of pyrocumulonimbus (pyroCb) storms, roughly 75 km apart, erupted simultaneously in the forests of Wollemi and Blue Mountains National Parks. The so-named Wollemi and Grose Valley fires blew up at an unusual time-late morning-and injected smoke into the uppermost troposphere. This is the first pyroCb event recorded during active pyroconvection by NASA's A-Train satellite constellation. Hence we show for the first time the pyroconvection column from simultaneous passive imagers, active lidar and radar, and UV backscattering instruments. There are no previous reports of pyroCb activity from Wollemi, and a report of the Grose Valley pyroconvective column limited its vertical extent to 6 km. Here we show, using ground-based radar data, that both fires blew up quasi-simultaneously before local noon. The Grose Valley pyroCb penetrated to the tropopause, the Wollemi pyroCb injection height exceeded the tropopause by 1-3 km. Analysis of a portion of the smoke plume sampled by the A-Train on 23 November confirms tropopause injection altitude. We explore a variety of meteorological observations and analyses to determine that the blow ups on 22 November 2006 (and only on this date in the fires' lifetimes) were mostly a consequence of anomalous boundary layer warmth and wind speed.


Xu Y.,Delaware State University | Jovanoski Z.,Applied and Industrial Mathematics Research Group | Bouasla A.,Annaba University | Triki H.,Annaba University | And 3 more authors.
Journal of Nonlinear Optical Physics and Materials | Year: 2013

This paper studies the dynamics of optical solitons in multi-dimensions with spatiooral dispersion and non-Kerr law nonlinearity. The integrability aspect is the main focus of this paper. Five different forms of nonlinearity are considered - Kerr law, power law, parabolic law, dual-power law and log law nonlinearity. The traveling wave hypothesis, ansatz approach and the semi-inverse variational principle are the integration tools that are adopted to retrieve the soliton solutions to the governing equation. As a result, several constraint conditions arise out of the integration process and represent necessary conditions for the existence of solitons. © 2013 World Scientific Publishing Company.


Wang G.-W.,Beijing Institute of Technology | Xu T.-Z.,Beijing Institute of Technology | Abazari R.,Islamic Azad University at Ardabil | Jovanoski Z.,Applied and Industrial Mathematics Research Group | And 2 more authors.
Acta Physica Polonica A | Year: 2014

We study the hybrid Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. Three different techniques - the ansatz method, Lie-symmetry analysis and the (G′/G)-expansion method - are used to find shock wave solutions. Several constraint conditions naturally emerge that guarantee the existence of shock waves. We discuss the nature of the solutions generated by the different methods.


Sullivan A.L.,CSIRO | Sharples J.J.,Applied and Industrial Mathematics Research Group | Matthews S.,CSIRO | Plucinski M.P.,CSIRO
Environmental Modelling and Software | Year: 2014

There is currently no fundamental understanding of the effects of topography on the behaviour of fires burning over a landscape. While a number of empirical models are employed operationally around the world, the effects of negative slopes on fire spread are ignored in all but one prediction system which may result in incorrect predictions. The general observation that large fires burning for some time over undulating topography can be approximated by assuming fire spread over flat ground is used to construct a quasi-empirical model framework for downslope rate of spread correction called kataburn. Kataburn is formulated for two alternative interpretations of slope spread-planar and linear-and can be applied to any empirical upslope spread correction model. Versions of kataburn derived using such models from Australia, the US and Canada are compared against experimental downslope data from the literature and found to better represent downslope spread than the existing operational downslope function. © 2014 Elsevier Ltd.


Triki H.,Annaba University | Jovanoski Z.,Applied and Industrial Mathematics Research Group | Biswas A.,Delaware State University | Biswas A.,King Abdulaziz University
Applied Mathematics and Information Sciences | Year: 2014

This paper obtains the solitary wave, shock wave as well as singular soliton solutions to the generalized Ostrovsky- Benjamin-Bona-Mahoney (gO-BBM) equation. The ansatz method is applied to obtain the solutions. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions. © 2014 NSP Natural Sciences Publishing Cor.


Safuan H.M.,Applied and Industrial Mathematics Research Group | Sidhu H.S.,Applied and Industrial Mathematics Research Group | Jovanoski Z.,Applied and Industrial Mathematics Research Group | Towers I.N.,Applied and Industrial Mathematics Research Group
Bulletin of Mathematical Biology | Year: 2013

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator-prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator-prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system's dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior. © 2013 Society for Mathematical Biology.


Triki H.,Annaba University | Jovanoski Z.,Applied and Industrial Mathematics Research Group | Biswas A.,Delaware State University | Biswas A.,King Abdulaziz University
Romanian Reports in Physics | Year: 2014

The dynamics of two-layered shallow water waves is studied in this paper by the aid of coupled potential-Korteweg-de Vries (pKdV) equation. There are two types of models that are considered. The first model yields solitary waves as well as shock wave solutions. The second model yields shock wave solutions only. The ansatz method is applied to retrieve the solitary wave as well as the shock wave solutions of both models. In both cases the time-dependent coefficients of dispersion and nonlinearity are considered, in order to keep the model closer to reality. Numerical simulations demonstrate the presence of soliton behaviour that is both rich and diverse.

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