
This paper studies the behavior of characteristics under partial prolongations. Partial prolongations define a natural equivalence relation between systems of partial differential equations [2], [3]. Examples are given to show that characteristics are not preserved in general. They are, however, preserved in an important case, namely, in determined or over-determined systems the highest-dimensional characteristics are proved to be invariant. A further example shows that even in determined systems lower-dimensional characteristics are not preserved.
partial differential equations
partial differential equations
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