Resurgent functions and nonlinear systems of differential and difference equations

2016/10/19 by Shingo Kamimoto, Kamimoto, Shingo
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Differential Equations and Dynamical Systems #Fractional Differential Equations Solutions

paper · pdf · doi:10.48550/arxiv.1610.05881

Abstract

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the method in arXiv:1610.05453. Using the estimates, we show the resurgence of formal series solutions of nonlinear differential and difference equations.

Related

• Nonlinear analysis with resurgent functions
• Nonlinear analysis with endlessly continuable functions
• Iterated convolutions and endless Riemann surfaces
• Introduction to 1-summability and resurgence
• Resurgence of the Euler-MacLaurin summation formula