Korteweg de Vries and nonlinear Schrödinger equations : qualitative theory of nonlinear the of solitons the the last 30 theory partial theory During years has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo to the observed example equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject are by known nonlinear At the the class of for same time currently example [89 94]). see the other there is solvable this method is narrow on hand PDEs sufficiently and by of differential The latter called the another qualitative theory equations. approach the of various in includes on pr investigations well posedness approach particular solutions such or lems for these the behavior of as stability blowing up equations these and this of approach dynamical systems generated by equations etc. properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study). Introduction Notation Evolutionary equations. Results on existance: The (generalized Korteweg de Vries equation (KdVE); The nonlinear Schrödinger equation (NLSE); On the blowing up of solutions; Additional remarks Stationary problems: Existence of solutions. An ODE approach; Existence of solutions. A variational method; The concentration compactness method of P.L. Lions; On basis properties of systems of solutions; Additional remarks Stability of solutions: Stability of soliton like solutions; Stability of kinks for the KdVE; Stability of solutions of the NLSE nonvanishing as (x) to infinity; Additional remarks Invariant measures: On Gaussian measures in Hilbert spaces; An invariant measure for the NLSE; An infinite series of invariant measures for the KdVE; Additional remarks Bibliography Index.