Solutions of Non-linear Differential and Difference Equations with Superposition Formulas

1999/05/06 by Alexander V. Turbiner, Alexander Turbiner, P. Winternitz +3
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9905003

17 pages, REVTeX, submitted to Journ.Math.Phys

arxiv created 1999/05/06 · arxiv updated 2009/11/30

Abstract

Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit solutions of certain classes of scalar and matrix Riccati equations are presented as an illustration of the general results.

Related

• Discrete matrix Riccati equations with superposition formulas
• Nonlinear differential equations with exact solutions
• The Analytical General Solution of the Riccati Equation and Its Intrinsic Functions
• General Solution of Second Order Linear Ordinary Differential Equation
• Second-order linear differential equations associated to a Riccati equation of constant coefficients