Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 29, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X21501152
Keywords
Fractal Derivative; Two-Scale Transform; Variational Principle; He's Variational Method; Semi-Inverse Method
Funding
- Fundamental Research Funds for the Universities of Henan Province [NSFRF210324]
- Program of Henan Polytechnic University [B2018-40]
- Innovative Scientists and Technicians Team of Henan Provincial High Education [21IRTSTHN016]
- Key Project of Scientific and Technology Research of Henan Province [212102210224]
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This study proposes a modified equal width equation with fractal derivatives to study the motion morphology of ion-acoustic waves in plasma. By utilizing the fractal variational formulation and He's variational method, combined with a two-scale transform, the periodic and solitary wave solutions of the equation are successfully found, opening up new perspectives for the study of traveling wave theory in fractal space.
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.
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