Power Series Solutions of Non-Linear q-Difference Equations and the   Newton-Puiseux Polygon
  Adapting the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, we compute their power series solutions, study the properties of the set of exponents of the solutions and give a bound for their $q-$Gevrey order in terms of the order of the original equation. 
Jos\'e Cano and Pedro Fortuny Ayuso
math.AG