What is the Method of Characteristics in Teaching Analytical Mechanics?

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This just to share a teaching experience.

Questions about the method of characteristics are raised from time to time in this forum.

Hope the following text will be of some use. This is what we tell to students in courses of
analytical mechanics :)
 

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What do you think of adding 2-3 examples and explaining the why's and ideas behind it, and write an insights article about it? The PDE are notoriously under represented.
 
Yes examples are missed I will add them.

UPD: Text is replaced; a discussion about the Hopf equation is added.
 
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