Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies

摘要

The Miura and anti-Miura transformations between the q -deformed KP and the q -deformed modified KP hierarchies are investigated in this paper. Then the auto-Backlund transformations for the q -deformed KP and q -deformed modified KP hierarchies are constructed through the combinations of the Miura and anti-Miura transformations. And the corresponding results are also generalized to the constrained cases. At last, some examples of Miura and auto-Backlund transformations are given.