Strain Wave Equation Research Articles

Bright and dark soliton solutions of the strain wave equation in microstructured solids

By using the approach of dynamical system, the exact traveling wave solutions of the strain wave equation in microstructured solids are solved. As results, all kinds of phase portraits in the parametric space are shown. The exact solutions are obtained including bright and dark soliton solutions. With the aid of Maple, the graphical representations and physical explanations of the bright and dark soliton solutions are given.

Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids

AbstractThe aim of this paper is to obtain the exact solutions of the strain wave equation applied for illustrating wave propagation in microstructured solids. The effective Kudryashov and functional variable methods along with the symbolic computation system have been used to accomplish the purpose.

English

The modeling of wave propagation in microstructure materials should be able to account for the various scales of microstructure. In this paper, the extended trial equation method was modified to construct the traveling wave solutions of the strain wave equation in microstructure solid. Some new different kinds of traveling wave solutions was gotten as, hyperbolic functions, trigonometric functions, Jacobi elliptic functions and rational functional solutions for the nonlinear strain wave equation when the balance number is positive integer. The balance number of this method is not constant and changes by changing the trial equation. These methods allow us to obtain many types of the exact solutions. By using the Maple software package, it was noticed that all the solutions obtained satisfy the original nonlinear strain wave equation. Key words: Strain wave equation, extended trial equation method, exact solutions, balance number, soliton solutions, Jacobi elliptic functions.

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, non-topological 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.

General traveling wave solutions of the strain wave equation in microstructured solids via the new approach of generalized (G′/G)-expansion method

The new approach of generalized (G′/G)-expansion method is significant, powerful and straightforward mathematical tool for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) arise in the field of engineering, applied mathematics and physics. Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this article, the new approach of generalized (G′/G)-expansion method has been applied to construct general traveling wave solutions of the strain wave equation in microstructured solids. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering fields.

A Generalized and Improved (G′/G)‐Expansion Method for Nonlinear Evolution Equations

A generalized and improved (G′/G)‐expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov‐Kuznetsov‐Benjamin‐Bona‐Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.