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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Quadratic invariants for clusters of resonant wave triads

## Quadratic invariants for clusters of resonant wave triadsAdd to your list(s) Download to your calendar using vCal - Nazarenko, S (University of Warwick
- Thursday 20 December 2012, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Kathryn de Ridder. Topological Dynamics in the Physical and Biological Sciences We consider clusters of interconnected resonant triads arising from the Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a linearly independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix A with entries 1, -1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J = N – M This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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