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In this paper, we studied the space-time fractional classical Drinfeld's Sokolov-Wilson (FDSW) system. This system does not have a Lagrangian. Noether's approach was used to derive the conservation laws in U and V variables. Finally, by reverting back to our original variables u and v; we obtained the conservation laws for the space-time fractional of classical Drinfeld's Sokolov-Wilson (FDSW) system. This conservation laws consisted of some local and nonlocal conserved vectors. [ABSTRACT FROM AUTHOR]

We study in this paper the Q-symmetry and conditional Q-symmetries of Drinfel'd-Sokolov-Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. [ABSTRACT FROM AUTHOR]

Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

The transient electromagnetic field generated by a vertical magnetic dipole above an atmospheric surface duct is investigated theoretically. The method used for the solution is essentially based on the application of which the two functions transform. Two integral transforms of the wave equation of Fitzgerald vector – a Laplace transform in time and a two-dimensional Fourier transform in the horizontal coordinates in space – are applied. This leads to an integral representation of the solution of the wave equation in the transform space, considering initial, boundary and transition conditions. Saddle point and residue methods are used to compute the integral. [Copyright &y& Elsevier]