Phase plane analysis for p-ultradiscrete system : infinite types of branching conditions (Mathematical structures of integrable systems, their developments and applications)

Abstract

The p-ultradiscrete procedure (ultradiscretization with parity variables) enables to ultradiscretize an equation with subtraction. Its feature is that a solution may have an infinite branches under certain conditions. Recently, an “approximative” technique by which such infinite branches may reduce to finite ones is proposed. In this article, a complicated situation for solutions of the p-ultradiscrete hard-spring equation is investigated, in which an infinite types of branching conditions appear. The approximative technique fairly summarizes the solutions and extends an understanding of the structure of solutions.