We point out that in certain cases, all the differential equations (for given indipendent and dependent variables) possessing a given symmetry necessarily share a common solution. Under weaker conditions, all such differential equations have a solution—in general, different for different equations—characterized by a common symmetry. We characterize this situation and the common solution, or the common symmetry of solutions, and give concrete examples.
Commuting-flow symmetries and common solutions to differential equations with common symmetries / G. Gaeta, P. Morando. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL. - ISSN 0305-4470. - 31:1(1998), pp. 337-347. [10.1088/0305-4470/31/1/029]
Commuting-flow symmetries and common solutions to differential equations with common symmetries
G. GaetaPrimo
;P. MorandoUltimo
1998
Abstract
We point out that in certain cases, all the differential equations (for given indipendent and dependent variables) possessing a given symmetry necessarily share a common solution. Under weaker conditions, all such differential equations have a solution—in general, different for different equations—characterized by a common symmetry. We characterize this situation and the common solution, or the common symmetry of solutions, and give concrete examples.Pubblicazioni consigliate
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