Characterizations of all real solutions for the KdV equation and WR

Abstract With the development of the study on nonlinear differential equations (NLDEs), more and more researchers consider exact meromorphic solutions of NLDEs in class W , which consists of elliptic function or their degeneration. It is meaningful to study the real-valued solutions of NLDEs. In this paper, we give characterizations of all real solutions for NLDEs in class W . As an example, we apply it to the KdV equation to show the sharpness of our results.