Novosibirsk State Technical University,

Kal Marx prosp. 20,

Novosibirsk 630092, RUSSIA

E-mail: dubrovsky@online.nsk.ru

**New lumps of Veselov-Novicov equation and new exact
rational potentials of Schroedinger equation with multiple pole wave functions
via $\overline\partial$-dressing method**

**Abstract:**

The scheme for calculating via Zakharov-Manakov $\overline\partial$-dressing
method of new rational solutions with constant asymptotic values at infinity
of the famous two-dimensional Veselov-Novikov (VN) integrable nonlinear
evolution equation and new exact rational potentials of two-dimensional
stationary Schroedinger (2DSchr) equation with multiple pole wave functions
is developed. As examples new lumps of VN nonlinear equation and new exact
rational potentials of 2DSchr equation with multiple pole of order two
wave functions are calculated. Among the constructed rational solutions
are as nonsingular and also singular.