According to the Lie theory, applying the third prolongation pr ( 3 ) V to (1), we can get the following system of symmetry equations: η α 0 + a u η x + a η u x + b η x x x = 0. (21).
The Lie point symmetries equation (3.1) is investigated in the reference [18].
Every Lie point, Lie-Bäcklund, and nonlocal symmetry of equation (3) provides a conservation law for this equation and the adjoint equation.
(ii) By virtue of the symmetry of equation (23) we can suppose that (Vert xVert ge Vert yVert ).
In similar ways, the model symmetry in Equation 14 allows two more matrix system rearrangements, where we have U l = H D p S 0 T A ¯ T + N ′ l , l= 1, …, L. (15) W m = S 0 T D m A ¯ H T + N ′ m, m = 1, …, 2 M. (16).
We give the following definition: We call approximate symmetries of equation (2) the (exact) symmetries of the system (9 - 10) through the one-parameter Lie group of infinitesimal transformations (11 - 14 11 - 14
The commutator table of the Lie point symmetries of equation (1) and the adjoint representations of the symmetry group of (1) on its Lie algebra are given in Table 1 and Table 2, respectively.
Even more than this rotational symmetry, the equations stay the same if I boost my speed.
In this study, we consider the partial Noether approach to analyze Noether symmetries of equation (3.1).
In case of symmetry the equations resemble with those of Grigolyuk.
When the above step fails (for equations that do not have the symmetries of equation (7)), it is still possible to transform a given equation to a form in which only the first derivative term has a constant coefficient.
