Partial differential equations
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A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment}
b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that {see attachments} where F and G are arbitrary functions of their arguments.
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Solution Summary
This shows how to classify and find general expressions for characteristic coordinates and use given canonical coordinates to transfer a partial differential equation to new coordinates.
Solution Preview
See attachment
a) Classify and find general expressions for the characteristic coordinates for the equation
( 1)
b) Use the canonical coordinates and and transfer the above PDE into the new coordinates. Solve it in the new coordinates and show that
where F and G are arbitrary functions of their arguments.
Solution:
a) The quadratic terms of the equation (1) are:
The corresponding characteristic equation is:
( 2)
( 3)
Since , the PDE is of hyperbolic type and ...
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