New solution of the N=2\mathcal{N}=2 Supersymmetric KdV equation via Hirota methods

We consider the resolution of the $\mathcal{N}=2$ supersymmetric KdV equation with $a=-2$ ($SKdV_{a=-2}$) from the Hirota formalism. For the first time, a bilinear form of the $SKdV_{a=-2}$ equation is constructed. We construct multisoliton solutions and rational similarity solutions.Comment: 7 pages, 9 figures. arXiv admin note: significant text overlap with arXiv:1104.059

Discretisations of constrained KP hierarchies

We present a discrete analogue of the so-called symmetry reduced or `constrained' KP hierarchy. As a result we obtain integrable discretisations, in both space and time, of some well-known continuous integrable systems such as the nonlinear Schroedinger equation, the Broer-Kaup equation and the Yajima-Oikawa system, together with their Lax pairs. It will be shown that these discretisations also give rise to a discrete description of the entire hierarchy of associated integrable systems. The discretisations of the Broer-Kaup equation and of the Yajima-Oikawa system are thought to be new.Comment: Accepted for publication in Journal of Mathematical Sciences, The University of Toky