Electron plasma waves excited and/or modified by finite objects such as laser and charged particle pulses are investigated nonperturbatively using a simple model where the driver is unaffected by the interaction. It is shown that smooth as well as sharply peaked electron plasma wake waves of large amplitude can exist. In particular, two charged pulses moving in tandem can excite a highly localized electron plasma wave without producing the expected long wake wave, a configuration that should be particularly useful for efficient trapping and acceleration of electrons to high energies.
