Hi Alesh,
I don't think the idea is to dissolve the pain, but to give people a means of overcoming despair and misery - pretty much the same idea with meditation generally. The natural feeling for many people with chronic pain is that happiness or even willingness to live is dependent on a solution for physical pain, which may not be forthcoming. I think meditation can help change that perspective.
The Blessed One said, "When touched with a feeling of pain, the uninstructed run-of-the-mill person sorrows, grieves, & laments, beats his breast, becomes distraught. So he feels two pains, physical & mental. Just as if they were to shoot a man with an arrow and, right afterward, were to shoot him with another one, so that he would feel the pains of two arrows; in the same way, when touched with a feeling of pain, the uninstructed run-of-the-mill person sorrows, grieves, & laments, beats his breast, becomes distraught. So he feels two pains, physical & mental....
"Now, the well-instructed disciple of the noble ones, when touched with a feeling of pain, does not sorrow, grieve, or lament, does not beat his breast or become distraught. So he feels one pain: physical, but not mental. Just as if they were to shoot a man with an arrow and, right afterward, did not shoot him with another one, so that he would feel the pain of only one arrow. In the same way, when touched with a feeling of pain, the well-instructed disciple of the noble ones does not sorrow, grieve, or lament, does not beat his breast or become distraught. He feels one pain: physical, but not mental.
Yet there is evidence that meditation can actually reduce pain:
Here Kelly McGonigal shares some MRI studies that demonstrate how this works (7 minutes):
http://www.youtube.com/watch?v=NQ2dK18--icBasically, experienced meditators have higher pain thresholds.
This is a review of studies of the effects of meditation on pain, showing that there are specific effects - i.e. not just placebo - of meditation on pain processing.
http://www.jneurosci.org/content/31/36/12705So, it seems to me some kind of meditation is an important option that should at least be presented to people with chronic pain.