On the integrability and solitons of the A± equation

Abstract

In this article the question of the integrability of the so-called A± equation is considered. Two powerful approaches, the Painlevé property and Hirota three-soliton test, are used as the integrability predictors. The A± equation is a new soliton equation with the MKdV-type soliton superposition formulae, but with richer nonlinear dynamics and richer soliton families. Also, explicit expressions for the multiple bell-shape and breather solitons are derived based on the Hirota substitution involved.