20 citations · 24 across the 5 of their papers we have counts for
5 papers
General Solutions of the Second-Kind Abel Equation
Ji-Xiang Zhao
The general solutions with free variable to the second-kind Abel equation, a nonlinear ordinary differential equation that has remained unsolved for nearly two centuries, are prese…
The Analytical General Solution of the Riccati Equation and Its Intrinsic Functions
Zhao Ji-Xiang
A sufficient and necessary condition for the integrability of the Riccati equation is established using the f elementary quadrature method. Based on this condition, an analytical g…
An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation
Ji-Xiang Zhao, Nan Li
Cosmic inflation can enter an ultraslow-roll (USR) stage, if there is a plateau on the inflaton potential. During this stage, the primordial curvature perturbation …
Primordial black holes and scalar-induced gravitational waves from the perturbations on the inflaton potential in peak theory
Ji-Xiang Zhao, Xiao-Hui Liu, Nan Li
A perturbation on the background inflaton potential can lead inflation into the ultraslow-roll stage and can thus remarkably enhance the power spectrum of th…
General Solutions of the Abel Differential Equations
Ji-Xiang Zhao
The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind.…