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This article aims to address the exact solution of the prestigious partial differential equation, namely, a double dispersive equation. Here, we are obtaining some new traveling wave solutions of the double dispersive equation with the more general mathematical technique, which is a direct algebraic extended method. This proposed technique is more general and integrated. The obtained solutions contain dark, bright, dark–bright, singular, periodic, kink, and rational function solutions. More illustration of traveling wave solutions of the double dispersive equation is given by plotting the two- and three-dimensional graphs with the suitable selection of parameters. This graphical presentation of solutions identifies the pattern of wave propagation. The acquired consequences are new and may play a significant role to examine the physical phenomena of wave propagation, where this model is used.

Propagation of some new traveling wave patterns of the double dispersive equation