Abstract
With the help of the Zakharov–Manakov \(\overline \partial \)-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 Schrodinger 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 Schrodinger stationary equation with multiple second-order poles are obtained.
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