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A systematic method for isolating certain nonlinear partial difference equations which are solvable by the method of inverse scattering is discussed. The equations are characterized by the dispersion relation (amplification factor) of the associated linearized equation. Corresponding to every neutrally stable linear scheme is a nonlinear difference equation which converges to an exactly solvable nonlinear evolution equation in the continuum limit. Explicit solition solutions are given.
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Ablowitz et al. (1977) studied this question.
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