Excellence in Research and Innovation for Humanity

International Science Index

Commenced in January 1999 Frequency: Monthly Edition: International Paper Count: 7

7
10006686
Group Invariant Solutions of Nonlinear Time-Fractional Hyperbolic Partial Differential Equation
Abstract:
In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.
Digital Article Identifier (DAI):
6
16740
Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method
Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Digital Article Identifier (DAI):
5
16742
Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation
Authors:
Abstract:

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

Digital Article Identifier (DAI):
4
9996665
Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method
Abstract:

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Digital Article Identifier (DAI):
3
14108
On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields
Abstract:
Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.
Digital Article Identifier (DAI):
2
1733
Exact Solutions of Steady Plane Flows of an Incompressible Fluid of Variable Viscosity Using (ξ, ψ)- Or (η, ψ)- Coordinates
Abstract:

The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating  that the flow equations possess an infinite set of solutions. 

Digital Article Identifier (DAI):
1
4739
Exact Solution of Some Helical Flows of Newtonian Fluids
Abstract:
This paper deals with the helical flow of a Newtonian fluid in an infinite circular cylinder, due to both longitudinal and rotational shear stress. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms and satisfy all imposed initial and boundary conditions. For large times, these solutions reduce to the well-known steady-state solutions.
Digital Article Identifier (DAI):
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