The construction of exact rational solutions with constant asymptotic values at infinity of two-dimensional NVN integrable nonlinear evolution equations via the $\overline{\partial}$-dressing method

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The classes of exact rational solutions with constant asymptotic values at infinity of Nizhnik-Veselov-Novikov (NVN) equations via the -dressing method of Zakharov and Manakov are constructed. At fixed time such solutions are the transparent (exactly solvable) potentials for one-dimensional Klein-Gordon or two-dimensional stationary Schrodinger equations. Among the constructed solutions are singular and also non-singular ones.