The Cauchy problem for the Pavlov equation with large data

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.

References in corpus (4)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
• A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
• The Cauchy Problem of the Ward equation