On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations - Nonlinear Sciences > Exactly Solvable and Integrable Systems - Download this document for free, or read online. Document in PDF available to download.

Abstract: Continuing our study on the complete integrability of nonlinear ordinarydifferential equations, in this paper we consider the integrability of a systemof coupled first order nonlinear ordinary differential equations ODEs of bothautonomous and non-autonomous types. For this purpose, we modify the originalPrelle-Singer procedure so as to apply it to both autonomous and non-autonomoussystems of coupled first order ODEs. We briefly explain the method of findingintegrals of motion time independent as well as time dependent integrals fortwo and three coupled first order ODEs by extending the Prelle-SingerPSmethod. From this we try to answer some of the open questions in the originalPS method. We also identify integrable cases for the two dimensionalLotka-Volterra system and three-dimensional R$\ddot{o}$ssler system as well asother examples including non-autonomous systems in a straightforward way usingthis procedure. Finally, we develop a linearization procedure for coupled firstorder ODEs.



Author: V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan

Source: https://arxiv.org/







Related documents