Exactly Solvable Quadratic Differential Equation Systems Through Generalized Inversion

• Ádám Bácsi ^[2] ; Albert Tihamér Kocsis ^[1]
  1. [1] Széchenyi István University

     Széchenyi István University

     Hungría

     
  2. [2] Széchenyi István University & Budapest University of Technology and Economics
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We study the autonomous systems of quadratic differential equations of the form x˙i(t)=x(t)TAix(t)+vTix(t) with x(t)=(x1(t), x2(t),…,xi(t),…) which, in general, cannot be solved exactly. In the present paper, we introduce a subclass of analytically solvable quadratic systems, whose solution is realized through a multi-dimensional generalization of the inversion which transforms a quadratic system into a linear one. We provide a constructive algorithm which, on one hand, decides whether the system of differential equations is analytically solvable with the inversion transformation and, on the other hand, provides the solution. The presented results apply for arbitrary, finite number of variables.