The N=2 supersymmetric KdV equations are studied within the framework of Hirota bilinear method. For two such equations, namely N=2, a=4 and N=2, a=1 supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear Bcklund transformation is given for the N=2, a=1 supersymmetric KdV equation.
In this paper, the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2.1. Using this transformation, families of surfaces with constant mean curvature from known ones can be constructed.
In this article, using the WDVV equation, the author first proves that all Gromov-Witten invariants of blowups of surfaces can be computed from the Cromov- Witten invariants of itself by some recursive relations. Furthermore, it may determine the quantum product on blowups. It also proves that there is some degree of functoriality of the big quantum cohomology for a blowup.
