Add to ORKGAnalytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis –long waves– over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, the linear shallow-water wave equation is solved for a flat ocean bottom for initial waves having finite-crest length. Analytical verification of source focusing is presented. The role of focusing in unexpectedly high tsunami runup observat...