Compactons versus Solitons

TL;DR

This paper explores PT-symmetric extensions of generalized Korteweg-de Vries equations, identifying conditions under which they admit both compacton and soliton solutions, and linking integrability to the Painleve test results.

Contribution

It demonstrates that models passing the Painleve test admit both compactons and solitons, establishing a connection between integrability and solution types.

Findings

Models with stable compactons fail the Painleve test and lack solitons.

Models with amplitude-dependent width pass the Painleve test and admit solitons.

Passage of the Painleve test indicates integrability of the models.

Abstract

We investigate whether the recently proposed PT-symmetric extensions of generalized Korteweg-de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painleve test fails, such that no soliton solutions can be found. The Painleve test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently these models admit soliton solutions in addition to compactons and are integrable.