Symmetries of differential-equations.4.



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González López, Artemio and Gonzalez Gascón, F. (1983) Symmetries of differential-equations.4. Journal of mathematical physics, 24 (8). pp. 2006-2021. ISSN 0022-2488

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By an application of the geometrical techniques of Lie, Cohen, and Dickson it is shown that a system of differential equations of the form [x^(r_i)]_i = F_i; (where r_i > 1 for every i = 1 , ... ,n) cannot admit an infinite number of pointlike symmetry vectors. When r_i = r for every i = 1, ... ,n, upper bounds have been computed for the maximum number of independent symmetry vectors that these systems can possess: The upper bounds are given by 2n _2 + nr + 2 (when r> 2), and by 2n_2 + 4n + 2 (when r = 2). The group of symmetries of ͞x_r = 0͞͞ (r> 1) has also been computed, and the result obtained shows that when n > 1 and r> 2 the number of independent symmetries of these equations does not attain the upper bound 2n_ 2 + nr + 2, which is a common bound for all systems of differential equations of the form x͞_r = F͞ (t, x͞, ... ,͞x (r - 1 ) when r> 2. On the other hand, when r = 2 the first upper bound obtained has been reduced to the value n_2 + 4n + 3; this number is equal to the number of independent symmetry vectors of the system ¨x͞ = 0͞, and is also a common bound for all systems of the form x͞ = F͞ (t, x͞, x͞).

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© 1983 American Institute of Physics.
It is a pleasure to express our gratitude to Dr. C. Ruiz and Dr. M. Amores for useful discussions with them and for providing some bibliography. It is also a pleasure to acknowledge the constant encouragement given by M. C. Hidalgo-Brinquis.

Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32903
Deposited On:27 Aug 2015 08:48
Last Modified:10 Dec 2018 15:10

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