Propagation of nonlinear longitudinal-transverse waves along magnetic fluxtubes in the solar atmosphere III. Modified equation of motion

In this series of papers the time-dependent propagation of nonlinear longit udinal-transverse waves in thin vertical magnetic flux tubes embedded in th e solar atmosphere is investigated numerically using the (one-dimensional) thin tube approximation. As in the last decade the particular form of the b ackreaction term in the transverse equation of motion has been under consid erable dispute we investigate this issue once again and suggest a new expre ssion for the backreaction term in the local approximation. This new expres sion intends to avoid criticisms leveled at the previous terms. In the pres ent paper we numerically compare the actual effects these different terms p roduce in a number of cases including the situations where the reported dis crepancies are prominent. We find that noticeable discrepancies between the various proposed backreaction terms occur only, when strong longitudinal f luid flows are present simultaneously with the swaying of the tube and that for weak flows these discrepancies disappear. If only weak longitudinal fl ows occur it thus appears that the particular choice of the backreaction te rm is not important.