Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon

TL;DR

This paper extends the Newton-Puiseux Polygon method to nonlinear q-difference equations, enabling the computation of power series solutions, analyzing their exponents, and bounding their q-Gevrey order.

Contribution

It adapts the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, providing new tools for solution analysis.

Findings

Computed power series solutions for nonlinear q-difference equations

Analyzed the properties of solution exponents

Provided bounds for q-Gevrey order based on equation order

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 $q-$Gevrey order in terms of the order of the original equation.