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The real and complex Lorenz equations in rotating fluids and lasers. (English) Zbl 1194.76280

Summary: The Lorenz equations are derived systematically from amplitude equations of weakly nonlinear dispersively unstable physical systems near criticality when weak dissipation is added. This derivation is only valid if the undamped neutral curve is not destabilised by the addition of weak dissipation. The addition of extra weak dispersive effects make some of the coefficients complex and yields a complex set of Lorenz equations. Both sets of equations are derived in examples in laser optics and baroclinic instability.

MSC:

76U05 General theory of rotating fluids
78A60 Lasers, masers, optical bistability, nonlinear optics
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