Construction of New Exact Rational Solutions to the Veselov–Novikov Equation and New Exact Rational Potentials for the Two-Dimensional Schrödinger Stationary Equation by the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline \partial $$ \end{document}-Dressing Method

With the help of the Zakharov–Manakov \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overline \partial $$ \end{document}-dressing method, the scheme of obtaining exact rational solutions to the well-known two-dimensional Veselov–Novikov integrable nonlinear equation and exact rational potentials for the two-dimensional Schrödinger stationary equation corresponding to wave functions with multiple poles is developed. As an example, new exact rational nonsingular and singular solutions to the Veselov–Novikov equation and the corresponding exact rational potentials for the two-dimensional Schrödinger stationary equation with multiple second-order poles are obtained.