تقرير
Lie-Hamilton systems on the plane: Applications and superposition rules
| العنوان: | Lie-Hamilton systems on the plane: Applications and superposition rules |
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| المؤلفون: | Blasco, A., Herranz, F. J., de Lucas, J., Sardon, C. |
| المصدر: | J. Phys. A: Math. Theor. 48, 345202 (2015) |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics |
| الوصف: | A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of Hamiltonian vector fields with respect to a Poisson structure. We provide new algebraic/geometric techniques to easily determine the properties of such Lie algebras on the plane, e.g., their associated Poisson bivectors. We study new and known Lie-Hamilton systems on $\mathbb{R}^2$ with physical, biological and mathematical applications. New results cover Cayley-Klein Riccati equations, the here defined planar diffusion Riccati systems, complex Bernoulli differential equations and projective Schr\"odinger equations. Constants of motion for planar Lie-Hamilton systems are explicitly obtained which, in turn, allow us to derive superposition rules through a coalgebra approach. Comment: 33 pages. New contents added covering formalism, invariants and superposition rules |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1751-8113/48/34/345202 |
| URL الوصول: | http://arxiv.org/abs/1410.7336 |
| رقم الأكسشن: | edsarx.1410.7336 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1751-8113/48/34/345202 |
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