Nonlinear self-adjointness and conservation laws
By Nail H. Ibragimov. 2011
361 citations recorded by the source corpus.
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 − Δu = 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.
Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/15950c51795f89b56d4774e740a1bd8b22d9bc13
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Conservation laws for time-fractional subdiffusion and diffusion-wave equations (2014, background): “, definition 2 from [23]) can be extended to the timefractional diffusion equations.”