Abstract
The main purpose of this paper is to investigate the modified equal width-Burgers equation that is used wildly to describe long wave propagation in nonlinear media with dispersion and dissipation. With the help of the Semi inverse method, we successfully establish its generalized variational principle for the first time, which can reveal the energy conservation law of the whole solution domain. Then a novel and interesting method called He's frequency formulation, which is derived from the ancient Chinese algorithm (ACG)-Ying-Bu-Zu-Shu, is employed to construct its periodic solution. Finally, two examples are presented to illustrate the solutions in the form of 3-D and 2-D plots. The results in this work are expected to give certain guiding significance for the study of variational theory and periodic wave theory of physical equations.
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