The explicit structure of the prolongation algebra of the hirota-satsuma system

For a coupled system of KdV equations the prolongation Lie algebra is explicitly determined. It turns out to be of Kac-Moody type

Solutions of WDVV Equations in Seiberg-Witten Theory from Root Systems

We present a complete proof that solutions of the WDVV equations in Seiberg-Witten theory may be constructed from root systems. A generalization to weight systems is proposed

Symbolic computations in applied differential geometry

The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples have been included in the text to demonstrate the concrete manipulations in practice. In the appendix, a list of programs discussed in the paper is added

An upper bound for the ground-state energy of an antiferromagnetic chain with next-nearest-neighbor interaction

A trial function for the ground state of the antiferromagnetic linear chain leads to an equation for an upper bound of the ground-state energy per spin. This equation is solved exactly

Symmetries for the super-KdV equation: letter to the editor

Symmetries and higher-order or generalised symmetries for the SKdV equation are constructed. Moreover by the introduction of graded potentials a non-local generalised symmetry is obtained, leading to the recursion operator for symmetries in a straightforward way, without making use of the bi-Hamiltonian structure