Asymptotically exact evolution equations are derived for trains of small amplitude counterpropagating water waves over finite depth. Surface tension is included. The resulting equations are nonlocal and generalize the equations derived by Davey and Stewartson for unidirectional wave trains. The stability properties of stationary standing and quasiperiodic waves are determined as a function of surface tension and fluid depth for both long wavelength longitudinal and transverse perturbations.
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Pierce et al. (1994) studied this question.
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