Demonstration and Application Study on Non-integrability of Painleve Equations

Abstract

Abstract In this paper, it focuses to verify the non-integrability of Painleve Equations by the use of the traditional Lie group theory, and finds out a first integral of the class gyroscopic system. Thus proving the Lie group theory is an important tool to study whether a system is integrable, and through the application study of the differential-equation Lie group theory in the braiding technology proving the differentiating-equation Lie group theory is of high practical value, that is calculations in braided material stiffness and elastic modulus.