Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory

Details Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory

2007-03-14

arxiv.org/abs/math-ph/0703048v2

Physics

Mathematical Physics

30 pages, LaTeX

Scientific paper

10.1016/j.cnsns.2007.05.017

Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action principle: generalized Noether's theorem and Hamiltonian type equations. In the first case, we derive conservation laws in the form of continuity equations that consist of fractional time-space derivatives. Among applications of these results, we consider a chain of coupled oscillators with a power-wise memory function and power-wise interaction between oscillators. In the second case, we consider an example of fractional differential action 1-form and find the corresponding Hamiltonian type equations from the closed condition of the form.

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