Abstract
In this paper, within the scope of the local fractional derivative theory, bidirectional propagation system local fractional equations are researched. Compared with the unidirectional propagation of nonlinear waves in a pipeline, the bidirectional propagation system equations studied in this paper can better describe the propagation of nonlinear waves in a channel. This study is groundbreaking and offers more possibilities for the bidirectional propagation of nonlinear waves in the simulation pipeline. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of a fixed fractal dimension are discussed. It is proven that the local fractional nonlinear bidirectional wave equations can describe the interaction of fractal waves. It is also shown that the study of traveling wave solutions of nonlinear local fractional equations has important significance in mathematical physics.
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