Exact solutions of compressible plane potential flows—a new method

Exact Solutions of Compressible Flow Equations with Spherical Symmetry

In this paper, we construct spherically symmetric solutions of the equations of compressible flow, which are important in the theory of explosion waves in air, water, and other media. Following McVittie [1], we write a general solution form, in terms of velocity potential, as a product of a function of time and a function of a similarity variable. First, we find solutions to the equations of mo...

Compressible viscoelasticity: stability of solutions for homogeneous plane-Earth models

Exact solutions for wave-like equations by differential transform method

Differential transform method has been applied to solve many functional equations so far. In this article, we have used this method to solve wave-like equations. Differential transform method is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Some examples are prepared to show theefficiency and simplicity of th...

Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation

In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)-expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the Benjamin-Ono equation. It is est...

Exact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation

In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.