Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon
arXiv:1209.0295 · doi:10.1007/s12346-022-00656-0
Abstract
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 Gevrey order in terms of the order of the original equation.