Resonant solutions and breathers to the BKP equation

In this paper, we derive resonant and breather solutions from multi-soliton solutions of the B-type Kadomtsev–Petviashvili (BKP) equation of fourth order via the Hirota bilinear method. We first discuss N-soliton solutions of the BKP equation and use the linear superposition principle to generate N-resonant solutions. Subsequently, we construct complexiton and breather solutions and finally, study the dynamics of some selected solutions with the aid of 3D plots, contour plots and density plots.

     

Levels and sources of heavy metal contamination in road dust in selected major highways of Accra,Ghana

Environmental studies have revealed significant contributions of vehicular exhaust emissions to high pollution levels in urban dwellings. The levels and sources of heavy metal contaminations of some major roads in Accra have been investigated in this work. Street dust samples collected from four major roads in Accra (Mallam Junction‐Weija road, John Teye‐Pokuase road, Tema Motorway and Tetteh Quarshie Interchange in Accra) were analysed for their elemental concentrations using energy‐dispersive X‐ray fluorescence. Twenty elements were identified: K, Ca, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr and Pb. Significant concentration levels were obtained for K, Ca, Ti, V, Cr, Mn, Fe, Cu, Zn, Br, Rb, Sr, Y, Zr and Pb in all the samples and were used for the source identification. Enrichment factors and principal component analysis were used to verify the anthropogenic contribution to road dust. Results obtained for the enrichment factors showed moderate enrichment for V, Cr and Cu, while Zn, Br, Zr and Pb were significantly enriched. Principal component analysis identified four sources and their contributions to the elemental contents in the road dust. Natural crust, brake wear, tyre wear and vehicle exhaust emission were the four sources identified. The contribution of vehicular non‐exhaust emissions to heavy metal contamination in the road dust was found to be greater than that of exhaust emissions. Copyright © 2012 John Wiley & Sons, Ltd.     

Complexiton solutions to the Hirota‐Satsuma‐Ito equation

The Hirota bilinear method is a powerful tool for solving nonlinear evolution equations. Together with the linear superposition principle, it can be used to find a special class of explicit solutions that correspond to complex eigenvalues of associated characteristic problems. These solutions are known as complexiton solutions or simply complexitons. In this article, we study complexiton solutions of the the Hirota‐Satsuma‐Ito equation which is a (2 + 1)‐dimensional extension of the Hirota‐Satsuma shallow water wave equation known to describe propagation of unidirectional shallow water waves. We first construct hyperbolic function solutions and consequently derive the so‐called complexitons via the Hirota bilinear method and the linear superposition principle. In particular, we find nonsingular complexiton solutions to the Hirota‐Satsuma‐Ito equation. Finally, we give some illustrative examples and a few concluding remarks.