# Invariant tori, action-angle variables, and phase space structure of the Rajeev-Ranken model

@article{Krishnaswami2019InvariantTA, title={Invariant tori, action-angle variables, and phase space structure of the Rajeev-Ranken model}, author={Govind S. Krishnaswami and T. R. Vishnu}, journal={Journal of Mathematical Physics}, year={2019} }

We study the classical Rajeev-Ranken model, a Hamiltonian system with three degrees of freedom describing nonlinear continuous waves in a 1+1-dimensional nilpotent scalar field theory pseudodual to the SU(2) principal chiral model. While it loosely resembles the Neumann and Kirchhoff models, its equations may be viewed as the Euler equations for a centrally extended Euclidean algebra. The model has a Lax pair and r-matrix leading to four generically independent conserved quantities in…

## 2 Citations

Quantum Rajeev-Ranken model as an anharmonic oscillator

- Physics, Mathematics
- 2021

The Rajeev-Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves of wavenumber k in a scalar field theory pseudodual to the 1+1D SU(2) principal chiral model. Classically,…

An introduction to Lax pairs and the zero curvature representation

- Physics, Mathematics
- 2020

Lax pairs are a useful tool in finding conserved quantities of some dynamical systems. In this expository article, we give a motivated introduction to the idea of a Lax pair of matrices $(L,A)$,…

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