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We proposed general scheme for construction of exact real periodicalsolutions of mKP-1 equation via Zakharov-Manakov $\overline{\partial}$-dressingmethod, derived convenient determinant formula for calculation of suchsolutions and demonstrated how reality and boundary conditions for the field$u(x,y,t)$ can be satisfied. We calculated the new classes of exact periodicalsolutions of mKP-1 equation: 1. the class of nonsingular one-periodic solutionsor nonlinear plane monochromatic waves; 2. the class of two-periodic solutionswithout imposition of any boundary condition; 3. the class of two-periodicsolutions with integrable boundary condition $u(x,y,t)\mid_{y=0}=0$. Weinterpreted the third class of two-periodic solutions with integrable boundarycondition obtained by the use of special nonlinear superpositions of two simpleone-periodical waves as eigenmodes of oscillations of the field $u(x,y,t)$ insemi-plane $y\geq 0$, the analogs of standing waves on the string with fixedendpoints.

New exact periodical solutions of mKP-1 equation via $\overline{\partial}$-dressing