Integrable models from PT-symmetric deformations

TL;DR

This paper investigates whether PT-symmetric deformations can preserve integrability in models like Burgers and Korteweg-De Vries, using the Painleve test to identify integrable deformations and establish new integrable models.

Contribution

It demonstrates that PT-symmetric deformations can preserve integrability in Burgers equation and constructs specific deformations passing the Painleve test, advancing understanding of integrable PT-symmetric models.

Findings

Burgers equation admits infinitely many PT-symmetric deformations passing the Painleve test.

A specific convergent Painleve expansion is established for Burgers deformations.

Korteweg-De Vries deformations do not generally pass the Painleve test, but a defective expansion is constructed.

Abstract

We address the question of whether integrable models allow for PT-symmetric deformations which preserve their intgrability. For this purpose we carry out the Painleve test for PT-symmetric deformations of Burgers and the Korteweg-De Vries equation. We find that the former equation allows for infinitely many deformations which pass the Painleve test. For a specific deformation we prove the convergence of the Painleve expansion and thus establish the Painleve property for these models, which are therefore thought to be integrable. The Korteweg-De Vries equation does not allow for deformations which pass the Painleve test in complete generality, but we are able to construct a defective Painleve expansion.