On local existence of solutions for nonlinear systems of Cauchy-Riemann operator of any order in the plane

TL;DR

This paper establishes a general local existence theorem for nonlinear systems of Cauchy-Riemann operators of any order in the complex plane, extending the analogy of local existence results known for ordinary differential equations.

Contribution

It introduces a broad local existence theorem for high-order nonlinear Cauchy-Riemann systems, generalizing classical results to complex PDEs.

Findings

Proves local existence for nonlinear high-order Cauchy-Riemann systems

Extends the analogy between ODEs and complex PDEs

Provides foundational results for further analysis of complex systems

Abstract

We prove a general local existence theorem for nonlinear systems of Cauchy-Riemann operator of any order in one complex variable with initial values at a given point, which is a counterpart of local existence of ODE.