A Geometric Approach to Burgers' Riccati Equation

摘要

The directrix approach, which gives powerful insight to the geometric structure of solutions of the general Riccati equation, is developed. Burgers' Riccati equation is derived, and conclusions are drawn using the directrix approach concerning the boundedness properties of solutions of this equation with certain restrictions on parameter values. Closed form solutions are developed for Burgers' Riccati equation for certain parameter values. A method is produced to obtain the vertical assymptote for unbounded solutions of Burgers' Riccati equation with certain restrictions on parameter values. Conclusions drawn from the application of the directrix method to Burgers' equation are verified. A research bibliography for Riccati's Equation is included. (Author)