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Zbl 1121.70014
Kara, A.H.; Mahomed, F.M.
Noether-type symmetries and conservation laws via partial Lagrangians. (English)
[J] Nonlinear Dyn. 45, No. 3-4, 367-383 (2006). ISSN 0924-090X; ISSN 1573-269X/e

Summary: We show how one can construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what we term partial Lagrangians. This is even in the case when a system does not directly have a usual Lagrangian, e.g. scalar evolution equations. These Noether-type symmetry operators do not form a Lie algebra in general. We specify the conditions under which they do form an algebra. Furthermore, we derive conditions under which they are symmetries of Euler-Lagrange-type equations. Examples are given including those that admit a standard Lagrangian such as Maxwellian tail equation, and equations that do not such as the heat and nonlinear heat equations. We also obtain new conservation laws from Noether-type symmetry operators for a class of nonlinear heat equations with more than two independent variables.

MSC 2000:: *70H33 Symmetries
70G65 Symmetries, Lie-group and Lie-algebra methods

Keywords: partial Lagrangians; Lie algebra; Euler-Lagrange equations

Cited in: Zbl 1130.70012 Zbl 1130.82028

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