Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 44, Issue 43, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/44/43/432002
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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 u(t) - Delta u = 0 becomes strictly self-adjoint after multiplying by u(-1). 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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