I solved the problem.
First you obtain a pointer to the scale division of the XBottom ax.
QwtScaleDiv* scdiv = axisScaleDiv(xBottom);

tick_lst= scdiv->ticks(QwtScaleDiv::MajorTick); // get the tick list

tick_lst.clear(); // clear the tick list

tick_list.push_back( value ) // insert new values

scdiv->setTicks(QwtScaleDiv::MajorTick,tick_lst); // put the tick list back on the ax

The tick_lst must be declared as private in the class.
I had several other bugs, i spent 2 days on this bug.