  Inspired by new trends in atomtronics, cold atoms devices and Bose-Einstein
condensate dynamics, we apply a general technique of N=4 extended
Supersymmetric Quantum Mechanics to isospectral Hamiltonians with triple-well
potentials, i.e. symmetric and asymmetric. Expressions of quantum-mechanical
propagators, which take into account all states of the spectrum, are obtained,
within the N = 4 SQM approach, in the closed form. For the initial Hamiltonian
of a harmonic oscillator, we obtain the explicit expressions of potentials,
wavefunctions and propagators. The obtained results are applied to tunneling
dynamics of localized states in triple-well potentials and for studying its
features. In particular, we observe a Josephson-type tunneling transition of a
wave packet, the effect of its partial trapping and a non-monotonic dependence
of tunneling dynamics on the shape of a three-well potential. We investigate,
among others, the possibility of controlling tunneling transport by changing
parameters of the central well, and we briefly discuss potential applications
of this aspect to atomtronic devices.
