Periodic waves of the non dissipative double dispersive micro strain wave in the micro structured solids

Abstract

The non dissipative double dispersive micro strain wave in the micro structured solid is solved via the F-expansion method and obtained the new exact doubly periodic Jacobi elliptic function solutions. The F-expansion method converts the nonlinear partial differential equation into ordinary differential equation, then the initially assumed solution converts the ordinary differential equation into systems of algebraic equations. By solving these algebraic equations, the six families of the periodic wave solutions are classified of which three are real valued and three are complex valued. Next by treating the Jacobi elliptic function modulus to 0 (or) 1, some of the new exact solitons and their classifications are obtained. The two dimensional and three dimensional graphs are plotted to show the traversing of the obtained wave trains.