Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications

Experiments on solitary waves.- Stimulated Raman and Brillouin scattering and the inverse method.- Direct method of finding exact solutions of nonlinear evolution equations.- Bäcklund transformations at the turn of the century.- The application of Bäcklund transforms to physical problems.- On applications of generalized Bäcklund transformations to continuum mechanics.- Some old and new techniques for the practical use of exterior differential forms.- Bäcklund transformation of potentials of the Korteweg-deVries equation and the interaction of solitons with cnoidal waves.- Pseudopotentials and their applications.- Variational problems and Bäcklund transformations associated with the sine-gordon and Korteweg-deVries equations and their extensions.- The interrelation between Bäcklund transformations and the inverse scattering transform.- Relation between Bäcklund transformations and inverse scattering problems.- Some comments on Bäcklund transformations, canonical transformations, and the inverse scattering method.