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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]

Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro-differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro-differential equations and Abel’s integral equations. [ABSTRACT FROM AUTHOR]

Explicit formulas for the magnetic field and divergence of multisolenoid Aharonov-Bohm potential are obtained; the mathematical essence of this potential is explained. It is shown that the magnetic field and divergence of this potential are very singular generalized functions concentrated at a finite number of thin solenoids. Deficiency index is found for the minimal operator generated by the Aharonov-Bohm differential expression. [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]

We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions are obtained. [ABSTRACT FROM AUTHOR]

We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian's decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented. [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]

In this work, we establish new exact solutions for the Hirota-Satsuma equations. New approach for the tanh is used and extended tanh methods to construct travelingwave solutions in terms of a hyperbolic tangent functions. New families of solitary wave solutions and periodic solutions are also obtained for Hirota-Satsuma equations. Our approach is reduce the size of the computational adopted in other techniques without any conditions to apply on any system of partial differential equations. [ABSTRACT FROM AUTHOR]

In this article, we study the nonlinear Euler equations with respect to the unknown functions . We use an extended hyperbola function method, tanh-function method and sec q - tanh q method to find some new solitary wave solutions of the nonlinear Euler equations. [ABSTRACT FROM AUTHOR]

In this paper, we find invariant solutions and soliton solutions for the nonlinear Euler equations with respect to the unknown functions G(x,y,t) and F(x,y,t). New dimensional reduction and exact solutions for nonlinear Euler equations are obtained. By using group analysis invariant solutions are given with respect to some forms of the unknown functions G(x,y,t) and F(x,y,t). We use the modified extended tanh- function to determine the soliton wave solutions for the nonlinear Euler equations. [ABSTRACT FROM AUTHOR]

A consequent application of the machinery of Lie group analysis to the equation of the one-dimensional motion of a gas under the influence of monochromatic radiation leads to the general group classification of the absorption coefficient. Classes of the solutions depending very strongly on the absorption coefficient will be discovered and discussed for some cases of the plane and cylindrical symmetry. [Copyright &y& Elsevier]

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]