Nail H . Ibragimov Selected Works
نویسندگان
چکیده
The object of the present lecture is the discussion of the group-theoretical nature of the conservation theorems for differential equations. To illustrate the use of the general conservation theorems the differential equations of mechanics are chosen.
منابع مشابه
Invariants for Evolution Equations
In the spirit of the recent work of Ibragimov [1] who adopted the infinitesimal method for calculating invariants of families of differential equations using the equivalence groups, we apply the method to evolution type equations of the form ut = f(x, u)uxx + g(x, u, ux). We show that the equivalence Lie algebra admitted by this equation has two functionally independent differential invariants ...
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The second-order ordinary differential equations can have one, two, three or eight independent symmetries. Sophus Lie showed that the equations with eight symmetries and only these equations can be linearized by a change of variables. Moreover he demonstrated that these equations are at most cubic in the first derivative and gave a convenient invariant description of all linearizable equations....
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In all areas of physics, conservation laws are essential since they allow us to draw conclusions of a physical system under study in an efficient way. Electrodynamics, in terms of the standard Maxwell electromagnetic equations for fields in vacuum, exhibit a rich set of symmetries to which conserved quantities are associated. Recently, there has been a renewed interest in the utilisation of suc...
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