Meissner equation
The Meissner equation is a linear ordinary differential equation that is a special case of Hill's equation with the periodic function given as a square wave. There are many ways to write the Meissner equation. One
is as
or
where
and is the Heaviside function shifted to. Another version is
The Meissner equation was first studied as a toy problem for certain resonance problems. It is also useful for understand resonance problems in evolutionary biology.
Because the time-dependence is piecewise linear, many calculations can be performed exactly, unlike for the Mathieu equation. When, the Floquet exponents are roots of the quadratic equation
The determinant of the Floquet matrix is 1, implying that origin is a center if
and a saddle node otherwise.
