Interpolating Dispersionless Integrable System

TL;DR

This paper introduces a new dispersionless integrable system that bridges the dispersionless KP and hyper-CR equations, derived from Einstein equations and related to Einstein-Weyl structures.

Contribution

It presents a novel integrable system interpolating between known equations, connecting symmetry reductions of Einstein equations and the Manakov-Santini system.

Findings

Defines a new dispersionless integrable system.

Establishes connections with Einstein--Weyl structures.

Shows the system as a symmetry reduction of Einstein equations.

Abstract

We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev-Petviashvili equation and the hyper-CR equation. The interpolating system arises as a symmetry reduction of the anti--self--dual Einstein equations in (2, 2) signature by a conformal Killing vector whose self--dual derivative is null. It also arises as a special case of the Manakov-Santini integrable system. We discuss the corresponding Einstein--Weyl structures.