VARIATIONAL PRINCIPLE FOR (2 + 1)-DIMENSIONAL BROER–KAUP EQUATIONS WITH FRACTAL DERIVATIVES
| Autor: | Ya-Nan Guo, Shi-Cheng Hou, Xiao-Qun Cao, Cheng-Zhuo Zhang, Ke-Cheng Peng |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Continuum mechanics 020209 energy Applied Mathematics One-dimensional space 02 engineering and technology 01 natural sciences Fractal dimension 010305 fluids & plasmas Nonlinear system Classical mechanics Fractal Variational principle Modeling and Simulation 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Geometry and Topology Porous medium |
| Zdroj: | Fractals. 28:2050107 |
| ISSN: | 1793-6543 0218-348X |
| DOI: | 10.1142/s0218348x20501078 |
| Popis: | This paper extends the [Formula: see text]-dimensional Broer–Kaup equations in continuum mechanics to its fractional partner, which can model a lot of nonlinear waves in fractal porous media. Its derivation is demonstrated in detail by applying He’s fractional derivative. Using the semi-inverse method, two variational principles are established for the nonlinear coupled equations, which up to now are not discovered. The variational formulations can help to study the symmetries and find conserved quantities in the fractal space. The obtained variational principles are proved correct by minimizing the functionals with the calculus of variations, and might find potential applications in numerical simulation. The procedure reveals that the semi-inverse method is highly efficient and powerful, and can be generalized to other nonlinear evolution equations with fractal derivatives. |
| Databáze: | OpenAIRE |
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