A periodic phase soliton of the ultradiscrete hungry Lotka–Volterra equation

Abstract

We propose a new type of solution to the ultradiscrete hungry Lotka–Volterra (uhLV) equation. For the solution, the periodic phase is introduced into the known soliton and the extended soliton becomes a traveling wave showing a periodic variation. We call this type of wave a ‘periodic phase soliton’ (PPS). The solution has two forms of expression: one is the ‘perturbation form’ and the other is the ‘ultradiscrete permanent form’. We analyze the interaction among PPSs and solitons. Moreover, we give the outline of proof to show that the solution satisfies the bilinear equation of the uhLV equation.