"Orbital dynamics satisfying the 4th-order stationary extended Fisher

Article Title

Orbital dynamics satisfying the 4th-order stationary extended Fisher–Kolmogorov equation

Authors

Rami Ahmad El-Nabulsi, Mathematics and Physics Divisions, Athens Institute for Education and Research, 8 Valaoritou Street, Kolonaki 10671, Athens, Greece

Keywords

nonlocal-in-time kinetic energy, 4th-order differential equations, quantization, complex-shift method

Abstract

In this study, we discuss the central force problem by using the nonlocal-in-time kineticenergy approach. At low length scales, the system is dominated by the generalized 4th-orderextended Fisher–Kolmogorov stationary equation and by the 4th-order stationary Swift–Hohenberg differential equation under explicit conditions. The energy is a conserved quantityalong orbits of the extended Fisher–Kolmogorov stationary equation. The system is quantized,the system is stable, and the ground energy problem is solved.