Abstract
In this paper nonlinear Schrödinger equation (NSE) is proposed to evaluate phononic wave propagation in nonlinear media regarding mass density as the fundamental parameter of nonlinearity. This equation is used to analyze the phononic wave limiting in one dimensional periodic structure. To approach this goal, considering the analogy, the mass density in elastic wave (EW) is related to the refractive index in electromagnetic (EM) wave and thus the nonlinear terms of the refractive index in EM correspond to nonlinear coefficient of the mass density in EW. Consequently, elastic wave coupled-mode (CM) equations are derived for backward and forward waves. Eventually, the CM equations are numerically solved to demonstrate the limiting process for phononic wave.
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