Magnons and spikes for $\mathcal{N}=2$ linear quivers and their non-Abelian T-duals

We compute the spectra associated with various semiclassical string states that propagate over $\mathcal{N}=2$ Gaiotto-Maldacena backgrounds. As an interesting special case, for the Abelian T- dual solution, we discover giant magnon and single spike configurations while imposing appropriate boundary conditions. However, for Sfetsos-Thompson backgrounds, one has to adopt a different string embedding which reveals ``modified'' dispersion relations both for magnons and spikes. These results boil down into the standard dispersion relations in the limit when the rank of the associated $SU(N_c)$ color gauge group becomes large enough. We further generalize our analysis in the presence of flavor D6 branes. Our analysis reveals a new set of dispersion relations, which shows that both magnons and spikes are ceased to exist in the presence of flavor excitations.