Abstract
With the help of symbolic computation, the Whitham-Broer-Kaup shallow water model is analyzed for its integrability through the Painlev´e analysis. Then, by truncating the Painlevé expansion at the constant level term with two singular manifolds, the Hirota bilinear form is obtained and the corresponding N-soliton solution with graphic analysis is also given. Furthermore, a bilinear auto-Bäcklund transformation is constructed for the Whitham-Broer-Kaup model, from which a one-soliton solution is presented.
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