On the integration of some classes of weakly deformed nonlinear Schrödinger equations

A method is proposed for constructing the solutions of a nonlinear Schrödinger equation with small corrections arising as a result of the introduction of arbitrary functions of the time and coordinates into the operator that dresses the kernel of a local \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\bar \partial $$ \end{document} problem.