On a complex differential Riccati equation
Analysis of PDEs
2009-11-13 v2 Classical Analysis and ODEs
Complex Variables
Abstract
We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schrodinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical "one-dimensional" results we discuss new features of the considered equation like, e.g., an analogue of the Cauchy integral theorem.
Cite
@article{arxiv.0706.1744,
title = {On a complex differential Riccati equation},
author = {Kira V. Khmelnytskaya and Vladislav V. Kravchenko},
journal= {arXiv preprint arXiv:0706.1744},
year = {2009}
}