Conservation laws and Hamilton’s equations for systems with long-range interaction and memory

✍ Scribed by Vasily E. Tarasov; George M. Zaslavsky

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 258 KB
• Volume: 13
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2007.05.017

✦ Synopsis

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.