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| 2. |
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Archives of ALGA, volume 1
- 2004
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Editorial collection (other academic/artistic)abstract
- Volume 1 contains 3 articles: Nail H. Ibragimov, Equivalence groups and invariants of linear and non-linear equations; Nail H. Ibragimov and Sergey V. Meleshko, Linearization of third-order ordinary differential equations; Nail H. Ibragimov, Gazanfer Ünal and Claes Jogreús, Group analysis of stochastic differential systems: Approximate symmetries and conservation laws.
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Archives of ALGA. Volume 2
- 2005
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Editorial collection (other academic/artistic)abstract
- Volume 2 contains 3 articles: Ilir Berisha, Translation of Bäcklunds paper ”Surfaces of constant negative curvature”; Johan Erlandsson, "Survey of mathematical models in biology from point of view of Lie group analysis"; Niklas Säfström, "Group analysis of a tumour growth model"
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Archives of ALGA. Volume 4
- 2007
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Editorial collection (other academic/artistic)abstract
- Volume 4 contains articles: Nail H. Ibragimov, Ewald J.H. Wessels and George F.R. Ellis, Group classication of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time; Nail H. Ibragimov A discussion of conservation laws for over-determined systems with application to the Maxwell equations in vacuum; Nail H. Ibragimov, Quasi-self-adjoint differential equations; Nail H. Ibragimov and Salavat V. Khabirov, Existence of integrating factors for higher-order ordinary differential equations; Nail H. Ibragimov, Integration of second-order linear equations via linearization of Riccati's equations; Nail H. Ibragimov and Sergey V. Meleshko Linearization of second-order ordinary differential equations by changing the order; Nail H. Ibragimov and Sergey V. Meleshko Second-order ordinary differential equations equivalent to y''= H(y); Nail H. Ibragimov, Sergey V. Meleshko and Supaporn Suksern, Linearization of fourth-order ordinary differential equations by point transformations; Nail H. Ibragimov and Emrullah Yasar, Non-local conservation laws in fluid dynamics
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Archives of ALGA, volume 7/8
- 2010
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Editorial collection (other academic/artistic)abstract
- Volume 7/8 contains 3 articles by N.H. Ibragimov, an article by N.H. Ibragimov, E. D. Avdonina and an article by N. H. Ibragimov , R. Khamitova.
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| 6. |
- Avdonina, Elena D., et al.
(author)
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Exact solutions of gasdynamic equations obtained by the method of conservation laws
- 2013
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In: Communications in nonlinear science & numerical simulation. - : Elsevier B.V.. - 1007-5704 .- 1878-7274. ; 18
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Journal article (peer-reviewed)abstract
- In the present paper, the recent method of conservation laws for constructing exact solutions for systems of nonlinear partial differential equations is applied to the gasdynamic equations describing one-dimensional and three-dimensional polytropic flows. In the one-dimensional case singular solutions are constructed in closed forms. In the threedimensional case several conservation laws are used simultaneously. It is shown that the method of conservation laws leads to particular solutions different from group invariant solutions.
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| 7. |
- Avdonina, Elena D., et al.
(author)
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Heat conduction in anisotropic media : Nonlinear self-adjointness and conservation laws
- 2012
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In: Discontinuity, Nonlinearity and Complexity. - : L & H Scientific Publishing. - 2164-6376. ; 1:3, s. 237-251
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Journal article (peer-reviewed)abstract
- 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 a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.
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| 8. |
- Boszhkov, Yuri, et al.
(author)
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Group analysis of the Novikov equation
- 2014
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In: Computational and Applied Mathematics. - : Springer. - 2238-3603 .- 1807-0302 .- 0101-8205. ; 33:1, s. 193-202
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Journal article (peer-reviewed)abstract
- 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 conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilation symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigate the invariant solutions.
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| 10. |
- Bruzon, MS, et al.
(author)
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Self-adjoint sub-classes of generalized thin film equations
- 2009
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In: Journal of Mathematical Analysis and Applications. - : Academic Press. - 0022-247X .- 1096-0813. ; 357:1, s. 307-313
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Journal article (peer-reviewed)abstract
- In this work we consider a class of fourth-order nonlinear partial differential equation containing several tin-specified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without Classical Lagrangians.
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