Geometrical Approaches to Differential Equations

Differential geometry as a tool for applied mathematicians.- Some heuristic comments on solitons, integrability conditions and lie groups.- On Bäcklund transformations and solutions to the 2+1 and 3+1 - dimensional sine - Gordon equation.- Bäcklund transformations.- Generalised Bäcklund 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 Bäcklund 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 singular perturbation problem.- The continuous Newton-method for meromorphic functions.- A precise definition of separation of variables.- Generation of limit cycles from separatrix polygons in the phase plane.- Normal solvability of linear partial differential operators in C?(?).- Connection problems for linear ordinary differential equations in the complex domain.- Periodic solutions of continuous self-gravitating systems.