Differential geometry as a tool for applied mathematicians.- Some heuristic comments on solitons, integrability conditions and lie groups.- On B¿lund transformations and solutions to the 2+1 and 3+1 - dimensional sine ¿ Gordon equation.- B¿lund transformations.- Generalised B¿lund transformations for integrable evolution equations associated with Nth order scattering problems.- Meromorphic forms solutions of completely integrable Pfaffian systems with regular singularities.- Far fields, nonlinear evolution equations, the B¿lund transformation and inverse scattering.- Convergence of formal power series solutions of a system of nonlinear differential equations at an irregular singular point.- Non-linear wave equations as hamiltonian systems.- How many jumps? Variational characterization of the limit solution of a