  We study features of tunneling dynamics in an exactly-solvable model of N=4
supersymmetric quantum mechanics with a multi-well potential and with broken
reflective symmetry. Quantum systems with a phenomenological potential of this
type demonstrate the phenomenon of partial localization of under-barrier
states, possibly resulting in the appearance of the so-called "resonant"
tunneling, or the phenomenon of coherent tunneling destruction, referring to
the complete localization. Taking the partial localization and the coherent
tunneling destruction as basic examples, we indicate main advantages of using
isospectral exactly-solvable Hamiltonians in studies quantum mechanical systems
with two- and three-well potentials. They, in particular, are: having enough
freedom of changing the potential shape in a wide range, that allows one to
choose an exactly-solvable model close to characteristics of the
phenomenological one; ability of changing the number of local minima and
symmetry characteristics of the potential (symmetric or deformed) without
changing the main part of the spectrum; engaging a smart basis of states, that
dramatically decreases the dimensionality of matrices used in the
diagonalization procedure of the corresponding spectral problem.
