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Infinite-dimensional hamilton-jacobi theory and l-integrability (2009).
| Content Provider | CiteSeerX |
|---|---|
| Author | Liu, Cheng-Shi |
| Abstract | The classical Liouvile integrability means that there exist n independent first integrals in involution for 2n-dimensional phase space. However, in the infinite-dimensional case, an infinite number of independent first integrals in involution don’t indicate that the system is solvable. How many first integrals do we need in order to make the system solvable? To answer the question, we obtain an infinite dimensional Hamilton-Jacobi theory, and prove an infinite dimensional Liouville theorem. Based on the theorem, we give a modified definition of the Liouville integrability in infinite dimension. We call it the L-integrability. As examples, we prove that the string vibration equation and the KdV equation are L-integrable. In general, we show that an infinite number of integrals is complete if all action variables of a Hamilton system can reconstructed by the set of first integrals. Keywords: Hamilton-Jacobi theory, Liouville integrability, the KdV equation, string vibration equation, integrable system. |
| File Format | |
| Publisher Date | 2009-01-01 |
| Access Restriction | Open |
| Subject Keyword | Infinite-dimensional Hamilton-jacobi Theory Liouville Integrability Kdv Equation Infinite Number Independent First Integral 2n-dimensional Phase Space First Integral Infinite Dimensional Hamilton-jacobi Theory Classical Liouvile Integrability Many First Integral Action Variable Hamilton System Infinite-dimensional Case Modified Definition Vibration Equation Hamilton-jacobi Theory Integrable System Infinite Dimensional Liouville Theorem Infinite Dimension String Vibration Equation |
| Content Type | Text |
