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Mathematics > Analysis of PDEs

arXiv:0706.1744 (math)
[Submitted on 12 Jun 2007 (v1), last revised 28 Sep 2007 (this version, v2)]

Title:On a complex differential Riccati equation

Authors:Kira V. Khmelnytskaya, Vladislav V. Kravchenko
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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.
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA); Complex Variables (math.CV)
MSC classes: 30G20; 35J10; 81Q05
Cite as: arXiv:0706.1744 [math.AP]
  (or arXiv:0706.1744v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.0706.1744
Journal reference: J. of Phys. A, 2008, v. 41, issue 8, 085205.
Related DOI: https://doi.org/10.1088/1751-8113/41/8/085205

Submission history

From: Vladislav V. Kravchenko [view email]
[v1] Tue, 12 Jun 2007 16:51:18 UTC (9 KB)
[v2] Fri, 28 Sep 2007 19:15:08 UTC (10 KB)
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