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17 papers
Symmetries and conservation laws of the generalized Krichever-Novikov equation
Stephen C. Anco, Elena D. Avdonina, Aliya Gainetdinova +3
A computational classification of contact symmetries and higher-order local symmetries that do not commute with , as well as local conserved densities that are not invariant u…
Heat conduction in anisotropic media: Nonlinear self-adjointness and conservation laws
Nail H. Ibragimov, Elena D. Avdonina
Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and…
Group Analysis of the Novikov Equation
Yuri Bozhkov, Igor Leite Freire, Nail H. Ibragimov
We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing cons…
Evolution equations of the second and third order with Lie-Bäcklund symmetries
Nail H. Ibragimov
Chapter 4 of my book [1] is dedicated to Lie-Bäcklund group analysis of various types of differential equations. The Russian edition of this book had an Addendum (pages 262-266) co…
Kadomtsev-Petviashvili equation: Nonlinear self-adjointness and conservation laws
Nail H. Ibragimov
The method of nonlinear self-adjointness is applied to the Kadomtsev-Petviashvili equation. The infinite set of conservation laws associated with the infinite algebra of Lie point…
Nonlinear self-adjointness in constructing conservation laws
Nail H. Ibragimov
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 p…