Riccati equation
It is a nonlinear first order ODE that was developed in the context of hydrodynamics. It is of the form
$$ u_1+p(x)u+q(x)u^2=f(x) $$Solution in a particular case:
There is a relation with Schrodinger equation, I think that Riccati equations are what satisfies the exponent of a solution of a Schrodinger equation...
A Riccati-type equation can be transformed into a second order linear homogeneous differential equation (see this. Moreover, it can be "approximately transformed" into a Schrodinger equation (see this.
________________________________________
________________________________________
________________________________________
Author of the notes: Antonio J. Pan-Collantes
INDEX: