New exact solutions of some Nonlinear partial differential Equations

Abstract

Mathematics is one of the popular, essential and fundamental method can be applied to represent various problems for finding exact solutions. Mathematics is used in various real-world problems of various domains from basic counting, drawing shapes to solving aeronautic problems. Problems may change its nature linearly or non-linearly. So, solving the linear and non-linear equations using a common method is not possible and never gives exact solution. Non-linear equations are highly applied for dynamically changing applications, hence not able to determine the exact results. newlineParallel to this, Homogeneous balance method has been applied broadly in various domains like mathematics, physics, chemistry for solving linear and non-linear equations. One of the most important application of homogeneous balance method is to explore various transformations, obtaining solitary wave solutions, reducing similarity in non-linear partial differential equations in physical mathematics. Homogeneous balance method has the ability to derive various transformations for non-linear partial differential equations having highest order partial derivatives. Due to the powerful impact, the homogeneous balance method is used to symbolically compute traveling wave solutions of some nonlinear wave and evolution equations. newlineThis research work absorbed on solving non-linear wave problems. The main objective of this research work is to attain an exact solution of non-linear equations by applying homogeneous balance method. In this research, the exact solutions of Gardner equation and Burgers equation are obtained by using homogeneous balance method and verified using MATHEMATICA. The performance of this research work is assessed by comparing with the other research works discussed in the literature survey. newline