By Peter E. Zhidkov

- of nonlinear the of solitons the the final 30 conception partial concept in the course of years - has into strategies of a sort a differential exact equations (PDEs) owning grown and in view the eye of either mathematicians box that draws physicists huge and of the of the issues of its novelty difficulties. actual very important purposes for within the into account are mo- to the saw, instance, equations major mathematical discoveries is the Makhankov one of many comparable V.G. via [60]. graph from this box tools that of convinced nonlinear via equations danger learning inverse those to the matter; equations have been learn quantum scattering constructed this system of the inverse referred to as solvable the scattering challenge (on topic, are via recognized nonlinear on the the category of for comparable time, at the moment instance [89,94]). see, the opposite there's solvable this system is slim available, PDEs sufficiently and, by means of of differential The latter referred to as the one other qualitative conception equations. technique, the of varied in comprises on pr- investigations well-posedness procedure specific options such or lems for those the habit of as balance blowing-up, equations, those and this of strategy dynamical structures generated via equations, etc., houses in wider type of a makes it to an difficulties (maybe attainable examine basically extra basic study).