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In this paper, a class of nonlinear algebraic differential equations (NADEs) is studied. The Painlevé analysis of the NADEs is considered. Abundant meromorphic solutions of the NADEs are obtained by means of the complex method. Then, meromorphic exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and (2+1)-dimensional sine-Gordon equation are derived via the applications of the NADEs.

Painlevé Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations