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We study dyonic solutions to the gravity-dilaton-antisymmetric form equationswith the goal of identifying new $p$-brane solutions on the fluxed lineardilaton background. Starting with the generic solutions constructed by reducingthe system to decoupled Liouville equations for certain values of parameters,we identify the most general solution whose singularities are hidden behind aregular event horizon, and then explore the admissible asymptotic behaviors. Inaddition to known asymptotically flat dyonic branes, we find two classes ofasymptotically non-flat solutions which can be interpreted as describingmagnetically charged branes on the electrically charged linear dilatonbackground (and the $S$-dual configuration of electrically charged branes onthe magnetically charged background), and uncharged black branes on thedyonically charged linear dilaton background. This interpretation is shown tobe consistent with the first law of thermodynamics for the new solutions.Comment: 17 page

Dyonic branes and linear dilaton background