| 1. |
- Anco, S., et al.
(författare)
-
Solutions of gasdynamic equations associated with classical and new conservation laws
- 2015
-
Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 268, s. 52-58
-
Tidskriftsartikel (refereegranskat)abstract
- Exact solutions of the one-dimensional gasdynamic equations are constructed by applying the method of conservation laws to all point-wise conserved vectors of the equations under consideration. © 2015 Elsevier Inc.
|
|
| 2. |
- Anco, S., et al.
(författare)
-
Symmetries and conservation laws of the generalized Krichever-Novikov equation
- 2016
-
Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 49:10
-
Tidskriftsartikel (refereegranskat)abstract
- A computational classification of contact symmetries and higher-order local symmetries that do not commute with t, x, as well as local conserved densities that are not invariant under t, x is carried out for a generalized version of the Krichever-Novikov (KN) equation. Several new results are obtained. First, the KN equation is explicitly shown to have a local conserved density that contains t, x. Second, apart from the dilational point symmetries known for special cases of the KN equation and its generalized version, no other local symmetries with low differential order are found to contain t, x. Third, the basic Hamiltonian structure of the KN equation is used to map the local conserved density containing t, x into a nonlocal symmetry that contains t, x. Fourth, a recursion operator is applied to this nonlocal symmetry to produce a hierarchy of nonlocal symmetries that have explicit dependence on t, x. When the inverse of the Hamiltonian map is applied to this hierarchy, only trivial conserved densities are obtained.
|
|
| 3. |
- Ibragimov, Nail, et al.
(författare)
-
Group classification and conservation laws of anisotropic wave equations with a source
- 2016
-
Ingår i: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 57:8
-
Tidskriftsartikel (refereegranskat)abstract
- Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.
|
|
| 4. |
- Ibragimov, Nail H., 1939-, et al.
(författare)
-
Group analysis of kinetic equations in a non-linear thermal transport problem
- 2015
-
Ingår i: International Journal of Non-Linear Mechanics. - : Pergamon Press. - 0020-7462 .- 1878-5638. ; 71, s. 1-7
-
Tidskriftsartikel (refereegranskat)abstract
- An application of modern group analysis to electron kinetic equations in non-linear thermal transport problem is discussed. The admitted symmetry group is calculated, and the optimal system of one and two-dimensional subalgebras is constructed. Representations of invariant solutions are presented.
|
|
