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In models with compact extra dimensions, where the Standard Model fields areconfined to a 3+1 dimensional hyperplane, the $t \bar t$ productioncross-section at a hadron collider can receive significant contributions frommultiple exchange of KK modes of the graviton. These are carefully computed inthe well-known ADD and RS scenarios, taking the energy dependence of the sumover graviton propagators into account. Using data from Run-I of the Tevatron,95% C.L. bounds on the parameter space of both models are derived. For Run-IIof the Tevatron and LHC, discovery limits are estimated.Comment: Typos corrected, references added. 12 pages, LaTeX, 2 ps figure

Special soliton structures in the (2+1)-dimensional nonlinear Schrödinger equation with radially variable diffraction and nonlinearity coefficients