On a complex differential Riccati equation

Details On a complex differential Riccati equation On a complex differential Riccati equation

2007-06-12

arxiv.org/abs/0706.1744v2

J. of Phys. A, 2008, v. 41, issue 8, 085205.

Mathematics

Analysis of PDEs

Scientific paper

10.1088/1751-8113/41/8/085205

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.

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