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 Mat. Zametki, 2008, Volume 84, Issue 6, Pages 874–881 (Mi mz4443)

Conservation Laws of Second Order for the Born–Infeld Equation and Other Related Equations

O. F. Men'shikh

S. P. Korolyov Samara State Aerospace University

Abstract: We describe a class of quasilinear partial differential equations of second order with two independent variables in the general case of mixed type for which we construct conservation laws of second order which are quadratic with respect to the second derivatives. As examples, we present similar conservation laws for the Born–Infeld equation, for the equations of minimal and maximal surfaces in Minkowski space, and for the classical equation of minimal surfaces.

Keywords: quasilinear partial differential equation, Born–Infeld equation, conservation laws of second order, Minkowski space, Abel equation, Laplace equation

DOI: https://doi.org/10.4213/mzm4443

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English version:
Mathematical Notes, 2008, 84:6, 814–820

Bibliographic databases:

UDC: 517.95

Citation: O. F. Men'shikh, “Conservation Laws of Second Order for the Born–Infeld Equation and Other Related Equations”, Mat. Zametki, 84:6 (2008), 874–881; Math. Notes, 84:6 (2008), 814–820

Citation in format AMSBIB
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