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Nonlinear self-adjointness and conservation laws
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2011 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 43Article in journal (Refereed) Published
Abstract [en]

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness (definition 1) and quasi-self-adjointness introduced earlier by the author. It is shown that the equations possessing nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint form. For example, the heat equation ut u = 0 becomes strictly self-adjoint after multiplying by u1. Conservation laws associated with symmetries are given in an explicit form for all nonlinearly self-adjoint partial differential equations and systems.

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IOP Science , 2011. Vol. 44, no 43
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URN: urn:nbn:se:bth-7216DOI: 10.1088/1751-8113/44/43/432002ISI: 000296147000002Local ID: diva2:834798
Available from: 2012-11-12 Created: 2011-12-28 Last updated: 2015-06-30Bibliographically approved

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