Computable Integrability. Chapter 1: General notions and ideas (original) (raw)

This chapter introduces foundational concepts of integrability theory within the realm of differential equations, focusing on computability aspects. It emphasizes the accessibility of integrability results for non-specialists, highlighting algorithmic approaches to categorizing and classifying integrable equations. The chapter delineates various definitions of integrability and examines classical classification methods, such as conservation laws and Lie symmetries, presenting examples to illustrate these distinctions.