Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/62411
Title: On multi-component ermakov systems in a two-layer fluid : integrable hamiltonian structures and exact vortex solutions
Authors: An, H
Kwong, MK
Zhu, H
Issue Date: 2016
Publisher: Wiley-Blackwell
Source: Studies in applied mathematics, 2016, v. 136, no. 2, p. 139-162 How to cite?
Journal: Studies in applied mathematics 
Abstract: By introducing an elliptic vortex ansatz, the 2+1-dimensional two-layer fluid system is reduced to a finite-dimensional nonlinear dynamical system. Time-modulated variables are then introduced and multicomponent Ermakov systems are isolated. The latter is shown to be also Hamiltonian, thereby admitting general solutions in terms of an elliptic integral representation. In particular, a subclass of vortex solutions is obtained and their behaviors are simulated. Such solutions have recently found applications in oceanic and atmospheric dynamics. Moreover, it is proved that the Hamiltonian system is equivalent to the stationary nonlinear cubic Schrodinger equations coupled with a Steen-Ermakov-Pinney equation.
URI: http://hdl.handle.net/10397/62411
ISSN: 0022-2526 (print)
1467-9590 (online)
DOI: 10.1111/sapm.12097
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