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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. Source

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. Source

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. Source

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. Source

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. Source

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