We study the formation of large-amplitude standing ion acoustic waves (SIAWs) by nonlinear phase-locking (autoresonance) with a weak, chirped frequency standing ponderomotive drive. These waves comprise a nonlinear two-phase solution, with each phase locked to one of the two traveling waves comprising the drive. The autoresonance in the system is guaranteed provided that the driving amplitude exceeds a threshold. The phenomenon is illustrated via water bag simulations within a nonlinear ion fluid model and analyzed using Whitham's averaged variational principle. The local ion and electron densities in the autoresonant SIAWs may significantly exceed the initial unperturbed plasma density and are only limited by kinetic wave-breaking.
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