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

Alexander Turbiner; Pavel Winternitz

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arXiv · solv-int/9905003

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

Alexander Turbiner·Pavel Winternitz

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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.

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Alexander Turbiner, Pavel Winternitz. 1999-05-06. Solutions of Non-linear Differential and Difference Equations with Superposition Formulas. https://arxiv.org/abs/solv-int/9905003

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