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