Phase plane analysis for ultradiscrete hard-spring equation with parity variables via standard central difference

Abstract Ultradiscretisation with parity variables is an extended version of ultradiscretisation. This extended procedure enables the treatment of difference equations with non-positive definite solutions. However, the uniqueness of the solution may be lost in specific situations. An approximative technique has been proposed to analyse such indeterminate solutions. In this study, the technique is applied to a non-integrable system, and the differences from an integrable case are studied. This approach provides a framework for analysing systems with indeterminate solutions, enabling advancements in understanding non-integrable behaviours.