LAUSR

In this article, we studied the problem of the Colombian potential perturbed by van der Waals potential interacting with combined electric and magnetic fields, known as Stark and Zeeman effects, and we determined new integrable cases by using the Painleve analysis for 2D integrability. This analysis contains three steps: Leading-order behaviors, resonances, and evaluation of arbitrary constants. We also determined the associated second integrals of motion. We verified the integrability of the problem in 3D, with determination of the integrals of motion. We justified the results by numerical investigations using the Poincare surfaces of the section, and we observed the transition chaos-order-chaos when we varied one of the system parameters.In this article, we studied the problem of the Colombian potential perturbed by van der Waals potential interacting with combined electric and magnetic fields, known as Stark and Zeeman effects, and we determined new integrable cases by using the Painleve analysis for 2D integrability. This analysis contains three steps: Leading-order behaviors, resonances, and evaluation of arbitrary constants. We also determined the associated second integrals of motion. We verified the integrability of the problem in 3D, with determination of the integrals of motion. We justified the results by numerical investigations using the Poincare surfaces of the section, and we observed the transition chaos-order-chaos when we varied one of the system parameters.