期刊
NONLINEAR DYNAMICS
卷 45, 期 3-4, 页码 367-383出版社
SPRINGER
DOI: 10.1007/s11071-005-9013-9
关键词
Lie-Backlund; Euler-Lagrange; Euler-Lagrange-type equations; Noether-type symmetry operators; partial Lagrangians; conservation laws
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, the conditions under which they are symmetries of the Euler-Lagrange-type equations are derived. Examples are given including those that admit a standard Lagrangian such as the 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 in more than two independent variables.
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