Symmetry analysis, bifurcation and exact solutions of nonlinear wave equation in semiconductors with strong spatial dispersion

Based on Lie symmetry analysis and steady bifurcation method, we study the nonlinear wave equation in semiconductors with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system and power series method. Then, steady bifurcation and solitary waves are presented. Especially, the existence and solvability of solitary or period wave are discussed, and all kinds of the solitary and period wave solutions are given by direct integration.