Share
Explore BrainMass

Partial differential equations

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.

Attachments

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 ...

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.

$2.19