arXiv subjects

I. Khames

Publications and source records attributed to I. Khames.

2 recordsLinked to original sources

arXiv2018

On graph Laplacian eigenvectors with components in {-1,0,1}

We characterize all graphs for which there are eigenvectors of the graph Laplacian having all their components in {-1,+1} or {-1,0,+ 1}. Graphs having eigenvectors with components in {-1,+1} are called bivalent and are shown to be the regular bipartite graphs and their extensions obtained by adding edges between vertices with the same value for the given eigenvector. Graphs with eigenvectors with components in {-1,0,+ 1} are called trivalent and are shown to be soft-regular graphs -graphs such that vertices associated with non-zero components have the same degree- and their extensions via some transformations.

math.SP↗

arXiv2018

Localized solutions of nonlinear network wave equations

We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest of the network satisfies a linear system forced by the excited node. This approximation is validated by reducing the nonlinear graph wave equation to the discrete nonlinear Schrodinger equation and by Fourier analysis. Finally, we examine numerically the condition for localization in the parameter plane, coupling versus amplitude and show that the localization amplitude depends on the maximal normal eigenfrequency.

nlin.PS↗