Quantum deformation of KdV hierarchies and their exact solutions: q-deformed solitons

A complete procedure is given by which one can construct q-deformed KdV hierarchies and obtain their exact solutions with arbitrarily many q-deformed solitons. As an elementary example, we obtain the exact solution of the q-deformed single soliton of the simplest (3,2) system, i.e. the q-deformed KdV equations, and investigate this solution in the case of small deformation. It is interesting that this method can supply many exact solutions for systems of new conventional nonlinear partial differential equations. (author)