Computable Integrability. Chapter 2: Riccati equation
Abstract
In this Chapter, using Riccati equation as our main example, we tried to demonstrate at least some of the ideas and notions introduced in Chapter 1  integrability in quadratures, conservation laws, etc. Regarding transformation group and singularities of solutions for RE, we constructed some equivalent forms of Riccati equation. We also compared three different approaches to the solutions of Riccati equation and its equivalent forms. The classical form of RE allowed us to construct easily asymptotic solutions represented by formal series. Linear equation of the second order turned out to be more convenient to describe finitegap potentials for exact solitonic solutions which would be a much more complicated task for a RE itself while generalization of solitonlike potentials to finitegap potentials demanded modified Schwarzian equation.
 Publication:

arXiv eprints
 Pub Date:
 September 2005
 arXiv:
 arXiv:mathph/0509024
 Bibcode:
 2005math.ph...9024K
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 This text is preliminary version of Chapter 2 of the ook "Computable Integrability", it consists of 31 pages