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A method for generating large-amplitude nonlinear plasma waves, which utilizes an optimized train of independently adjustable, intense laser pulses, is analyzed in one dimension both theoretically and numerically (using both Maxwell-fluid and particle-in-cell codes). Optimal pulse widths and interpulse spacings are computed for pulses with either square or finite-rise-time sine shapes. A resonant region of the plasma wave phase space is found where the plasma wave is driven most efficiently by the laser pulses. The width of this region, and thus the optimal finite-rise-time laser pulse width, was found to decrease with increasing background plasma density and plasma wave amplitude, while the nonlinear plasma wavelength, and thus the optimal interpulse spacing, increases. Also investigated are damping of the wave by trapped background electrons and the sensitivities of the resonance to variations in the laser and plasma parameters. Resonant excitation is found to be superior for electron acceleration to either beat-wave or single-pulse excitation because comparable plasma-wave amplitudes may be generated at lower plasma densities, reducing electron-phase detuning, or at lower laser intensities, reducing laser-plasma instabilities. Practical experimental methods for producing the required pulse trains are discussed.