Abstract
Ermakov-type systems in 2 + 1-dimensions are introduced. Multi-wave solutions of a 2 + 1-dimensional Pinney equation and a modulated 2 + 1-dimensional sine-Gordon equation are constructed via the standard Ermakov system. Lie group analysis of the latter is undertaken to reveal its underlying linear structure in terms of canonical coordinates. In conclusion, a 2 + 1-dimensional nonlinear system due to Stoker which arises in two-layer shallow water theory is shown to admit a symmetry reduction to a Ermakov system.
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