Have You Seen This PDE Before?

[Lurian]

In the course of my research I came across this PDE
$\frac{\partial{a_0}}{\partial{x}}\frac{\partial{a_1}}{\partial{y}}-\frac{\partial{a_0}}{\partial{y}}\frac{\partial{a_1}}{\partial{x}}=0.$
with both functions depending on x and y.
I am quite sure I have seen equations of this form before but I do not remember when and where. Maybe someone of you guys can help me?

Thanks

 

[pasmith]

In the course of my research I came across this PDE
$\frac{\partial{a_0}}{\partial{x}}\frac{\partial{a_1}}{\partial{y}}-\frac{\partial{a_0}}{\partial{y}}\frac{\partial{a_1}}{\partial{x}}=0.$
with both functions depending on x and y.
I am quite sure I have seen equations of this form before but I do not remember when and where. Maybe someone of you guys can help me?

Thanks

The left hand side is the determinant of the jacobian matrix
$$\left(<br /> \begin{array}{cc}<br /> \frac{\partial a_0}{\partial x} & \frac{\partial a_0}{\partial y} \\<br /> \frac{\partial a_1}{\partial x} & \frac{\partial a_1}{\partial y}<br /> \end{array}<br /> \right).$$

 

[jedishrfu]

isnt this also the curl of some vector function A(x,y,z) ?

∇ × A

the equation shown would be computing the z-component.