Abstract

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.