The known integrable models possess Schwarzian forms with M¨obious transformation invariance, it may be one of the best ways to find new inte grable models starting from some suitable Schwarzian forms. In this paper, with introducing the high dimensional Schwarzian derivatives, the general (n + 1)-dimensional systems are obtained from the usual (1+1)-dimensional Schwartzian Boussinesq equation. A singularity structure analysis of the extension system is carried out and it is shown that arbitrary dimensional systems admit the Painlev´e property. The single soliton and the traveling wave solutions of the model are studied.
Prof. Dr. Bilal BİLGİN