A new Lie systems approach to second-order Riccati equations

Details A new Lie systems approach to second-order Riccati equations A new Lie systems approach to second-order Riccati equations

2011-10-14

arxiv.org/abs/1110.3298v1

Int. J. Geom. Methods Mod. Phys. 9, 1260007 (2012)

Physics

Mathematical Physics

8 pages

Scientific paper

10.1142/S0219887812600079.

This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre transforms. This result allows us to construct new superposition rules for studying second-order Riccati equations and to reduce their integration to solving (first-order) Riccati equations.

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