Construction of new exact rational solutions to the veselov-novikov equation and new exact rational potentials for the two-dimensional schrodinger stationary equation by the (partial deriv)-bar-dressing method

摘要

With the help of the Zakharov-Manakov (partial deriv)-bar-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.