The N-soliton interactions in the adiabatic approximation for the MM (V (x) = 0) can be modelled by CTC .
The adiabatic approximation holds true for both equations if the soliton parameters satisfy :
This goal matches the needs of: (i) going beyond the simplest adiabatic approximation
-- commonly adopted in the description of ultrafast phenomena at the nanoscale; and(ii) dealing with the actual spatial inhomogeneities of many-electron systems at non-adiabatic level.
The authors use the Born-Oppenheimer adiabatic approximation
and show the parametric method for calculations for polyenes and acenes.
The time of flight was calculated for the proton and using the adiabatic approximation