Abstract
This work is interested in studying nondissipative double dispersive microstrain wave in the microstructured solids. Using a certain transformation, the basic equation is transformed into an ordinary differential equation that turns into a two-dimensional dynamical system corresponding to a one-dimensional Hamiltonian. Based on qualitative theory of dynamical systems, we consider some qualitative analyses of this system and use a conserved quantity to construct some traveling wave solutions. These solutions are illustrated graphically. We study the degeneracy of these solutions through the transmission between the orbits for different values of the included parameters. Moreover, we numerically study the quasiperiodic solution for the perturbed system after adding certain periodic forces to the main equation.