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Darboux and Analytic First Integrals of the Generalized Michelson System | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 8, Volume 18, Issue 2, December 2024, Pages 65-69 PDF (633.13 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2024.148978.1116 | ||
| Authors | ||
| Shno Farhad Mohammed* ; Kardo Baiz Othman | ||
| Department of Physics, College of Education - Shaqlawa, Salahaddin University - Erbil,Iraq | ||
| Abstract | ||
| The purpose of this work is to demonstrate that, for any value of a_1, a_2, and a_3, the generalized Michelson system u ̇= v,v ̇=w,w ̇= a_1 +a_2 v+ a_3 w-u^2/2 has neither a Darboux nor a rational first integral. Furthermore, we shall demonstrate that for a_3<0,√(2 a_1 ) >0 and a_3 a_2-√(2 a_1 ) >0, this system has no global C^1 first integrals. Additionally, the analytic first integral of this system for a generic condition is investigated near the equilibrium point (√(2 a_1 ),0,0). The purpose of this work is to demonstrate that, for any value of a_1, a_2, and a_3, the generalized Michelson system u ̇= v,v ̇=w,w ̇= a_1 +a_2 v+ a_3 w-u^2/2 has neither a Darboux nor a rational first integral. Furthermore, we shall demonstrate that for a_3<0,√(2 a_1 ) >0 and a_3 a_2-√(2 a_1 ) >0, this system has no global C^1 first integrals. Additionally, the analytic first integral of this system for a generic condition is investigated near the equilibrium point (√(2 a_1 ),0,0). | ||
| Keywords | ||
| Exponential factor; Darboux First Integral; Invariant Algebraic Surfaces; Analytic First Integral | ||
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