Excellence in Research and Innovation for Humanity

Nisha Goyal

Publications

2

Publications

2
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.
Keywords:
Gravitational fields, Lie Classical method, Exact solutions.
1
15030
Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method
Abstract:

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

Keywords:
Sawada-Kotera-Kadomtsev-Petviashivili equation, Bogoyavlensky-Konoplechenko equation,