Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I am working on an open source project that deals with the usage of lie groups to solve first order differential equations. For my reference, I am using this paper by Maple (It is there on this website http://arxiv.org/abs/gr-qc/9607037v1).

Basically the idea is to solve this PDE, $$\frac{\partial \eta}{\partial x} + (\frac{\partial \eta}{\partial y} - \frac{\partial \xi}{\partial x})*h - \frac{\partial \eta}{\partial x}*h^{2} - \xi*\frac{\partial h}{\partial x} - \eta*\frac{\partial h}{\partial y} = 0$$ for $\xi $ and $\eta$ where $h$ is a known function in $x$ and $y$

One of the assumptions made is $$\eta = f(y)$$ and $$\xi = g(x)$$

Applying it, the PDE simplifies to,

$$(\frac{df}{dy} - \frac{dg}{dx})*h - f*\frac{\partial h}{\partial x} - g*\frac{\partial h}{\partial y} = 0$$

Now the paper says, subdivide the equation into subexpressions involving only one of {f, g}. I first though that it meant, solving $$\frac{df}{dy}*h - f*\frac{\partial h}{\partial x} = 0$$ and $$-\frac{dg}{dx}*h - g*\frac{\partial h}{\partial y} = 0$$ individually. However that doesn't seem to be this case as, the example given in the paper doesn't satisfy this condition. I would like some help in interpreting what "subdivide the equation into subexpressions involving only one of {f, g}".

The mentioned method is on page 9 of the paper which is in the above mentioned website, if anyone is interested.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.