- 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).