The Cauchy problem for the Pavlov equation with large data

TL;DR

This paper develops a method to solve the Pavlov equation's Cauchy problem with large initial data by completing the inverse scattering theory and establishing short-time unique solvability.

Contribution

It introduces a Newtonian iteration scheme to solve a nonlinear Riemann-Hilbert problem, advancing the inverse scattering approach for the Pavlov equation.

Findings

Established short-time unique solvability for large initial data

Completed the inverse scattering theory for the Pavlov equation

Introduced a Newtonian iteration scheme for nonlinear Riemann-Hilbert problems

Abstract

The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a nonlinear Riemann-Hilbert problem via a Newtonian iteration scheme, we complete the inverse scattering theory and prove a short time unique solvability of the Cauchy problem of the Pavlov equation with large initial data.