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We extend our earlier study of special double limits of `boosted' $AdS_5$black hole solutions to include all black D$p$-branes of type II strings. Wefind that Lifshitz solutions can be obtained in generality, with varieddynamical exponents, by employing these limits. We then study such doublelimits for `boosted' D$p$-brane bubble solutions and find that the resultingnon-relativistic solutions instead describe Schr\"odinger like spacetimes,having varied dynamical exponents. We get a simple map between these Lifshitz &Schr\"odinger solutions and a relationship between two types of dynamicalexponents. We also discuss about the singularities of the Lifshitz solutionsand an intriguing thermodynamic duality.

Lifshitz/Schr\"odinger D-p-branes and dynamical exponents