We also have in mind that the inter-site Morse potential favours the excitation of soliton-like modes.
Coupling the inter-site Morse potential to the on-site Morse potential offers a variety of possibilities as the latter favours the onset of DB (for the case of on-site harmonic oscillations coupled to inter-site harmonic oscillations see  and references therein).
Note that, at variance with the Morse potential, DB are always possible with a 'hard' potential (frequency of small amplitude oscillations around minimum increases with increasing amplitude or spring stiffness increases with the widening of the separation; [x.
At a low to moderate level of excitation the Morse potential can be approximated by the Toda model and hence we shall make use of the known analytical solutions of the latter .
Before addressing the dynamics with Morse potentials it seems worth recalling results from the linear case.
On the other hand, Berrondo et al  employ the relationship between Morse potential and the two-dimensional harmonic oscillator to deduce the corresponding relation:
Matrix Elements for the Morse potential using ladder operators, Int.
Keywords Hypervirial theorem, coulomb and Morse potentials, langer transformation, matrix elements.
16] to incorporate the modified Morse potential function , to estimate elastic constants and stress-strain relationships of nanotubes under tensile and torsion loadings.
The modified Morse potential function  is simple and is used in the present study.
By incorporating the modified Morse potential function into an analytical molecular structural mechanics model, the mechanical responses of armchair and zigzag nanotubes in tension are investigated.