Abstract
Abstract: In this work we are interested in developing approximate models for water waves equation. We present the derivation of the new equations uses approximation of the phase velocity that arises in the linear water wave theory. We treat the (KdV) equation and similarly the C-H equation. Both of them describe unidirectional shallow water waves equation.
 At the same time, together with the (BBM) equation we propose, we provide the best approximation of the phase velocity for small wave numbers that can be obtained with second and third-order equations. We can extend the results of [3, 4]. A comparison between the methods is mentioned in this article.
 Key words: C-H equation, KdV equation, approximation, water wave equation, numerical methods.
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 [3]. D. J. Benney, “Long non-linear waves in fluid flows,” Journal of Mathematical 
 Physics, vol. 45, pp. 52–63, 1966. View at Google Scholar · View at Zentralblatt MATH
 [4]. Bezati, L., Hajrulla, S., & Hoxha, F. (2018). Finite Volume Methods for Non-Linear 
 Eqs. International Journal of Scientific Research and Management, 6(02), M- 2018.
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