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