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VARIATIONAL PRINCIPLE, SOLITARY AND PERIODIC WAVE SOLUTIONS OF THE FRACTAL MODIFIED EQUAL WIDTH EQUATION IN PLASMA PHYSICS

The unsmooth boundary will greatly affect the motion morphology of ion-acoustic waves in plasma, so a modified equal width equation with fractal derivatives is proposed. The fractal variational formulation of the problem is established by using the semi-inverse method, which provides the conservation laws in an energy form in the fractal space and reveals the possible solution structures of the equation. Then He’s variational method based on the variational theory and Ritz-like method, combined with the two-scale transform is used to seek the periodic and solitary wave solutions of the fractal modified equal width equation. The obtained results show that the variational method is simple but powerful, which is expected to open some new perspectives toward the study of traveling wave theory in fractal space.