Abstract
Here, we study a relation between discrete and continuum models on an example of the sine-Gordon and Φ4 equations. The analysis of various receptions of continualization in a linear case is carried out. The best approach allowing describing all spectrum of the discrete one-dimensional medium is chosen. Also, the nonlinear discrete sine-Gordon and Φ4 models are analyzed. The possibility of improvement of the known continuum approximations of these equations is shown.
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