An exponential expansion method and its application to the strain wave equation in microstructured solids

Abstract

The modeling of wave propagation in microstructured materials should be able to account for various scales of microstructure. Based on the proposed new exponential expansion method, we obtained the multiple explicit and exact traveling wave solutions of the strain wave equation for describing different types of wave propagation in microstructured solids. The solutions obtained in this paper include the solitary wave solutions of topological kink, singular kink, nontopological bell type solutions, solitons, compacton, cuspon, periodic solutions, and solitary wave solutions of rational functions. It is shown that the new exponential method, with the help of symbolic computation, provides an effective and straightforward mathematical tool for solving nonlinear evolution equations arising in mathematical physics and engineering. Ó 2014 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

On Travelling Wave Solutions of Dullin-Gottwald-Holm Dynamical Equation and Strain Wave Equation

“…( 2) by using generalized exponential rational function method [13]. M. G. Hafez and M. A. Akbar have obtained multiple explicit and exact traveling wave solutions of this equation by using an exponential expansion method [14].…”

Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model

“…Jacobi elliptic function scheme [7,8], extended simplest equation technique [9][10][11], Fexpansion method [12,13], trial equation scheme [14,15], various rational (𝐺 ′ /𝐺)-expansion tools [16][17][18], exp-function approach [19,20], improved tanh approach [21], Darboux transformation approach [22], different Hirota schemes [23][24][25][26][27], Kudryashov technique [28] etc. This present study is conducted by implementing two competent techniques such as improved tanh and improved auxiliary equation.…”

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

“…The remaining sections in our research paper are ordered as follows: Sect. 2 manipulates the extended exp-(-ϕ(ϑ))-expansion method [56][57][58][59][60] and the Jacobi elliptical function method [61][62][63] to procure novel solitary solutions of both suggested models. Section 5 gives the conclusion of this research.…”