Symmetry reductions and solutions to the Zoomeron equation

Abstract

The terms Boomeron and Zoomeron describe specific instances of solitons that have distinct features where they arise in various physical contexts particularly in laser physics, nonlinear optics and fluid mechanics. They are associated with the coupled Boomeron equation and its descendant the scalar Zoomeron equation (ZE). This article illustrates the application of the Lie theory of continuous groups to the (2+1)-dimensional version of the ZE governed by power-law nonlinearity. Closed-form solutions in terms of Airy functions and the imaginary error function are obtained and variations of the Lane–Emden equation are presented.