Symbol of a (non linear) differential operator

Question

I am interested in knowing whether there is a definition for the symbol of a PDO which is NOT linear. In Wikipedia and in the book I am reading (An Introduction to Partial Differential Equations by Renardy-Rogers) I only found the definition for linear PDOs.

Here is the Wikipedia link:

http://en.wikipedia.org/wiki/Symbol_of_a_differential_operator

Answer 1

The symbol of a nonlinear differential operator is defined as the symbol of its linearization.