Characteristic strip

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of a first-order partial differential equation

A family

of continuously-differentiable functions in an interval , satisfying the equations

where the multiplication of the vectors is the scalar product, and where


is a non-linear first-order partial differential equation in the unknown function . Here , , , , .

The importance of a characteristic strip consists in the fact that it is used in the study of, and in the search for, solutions of equation (*).

See also Characteristic.


[1] E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 2. Partielle Differentialgleichungen erster Ordnung für die gesuchte Funktion , Akad. Verlagsgesell. (1944)
[2] P. Hartman, "Ordinary differential equations" , Birkhäuser (1982)


A characteristic strip is sometimes called a bicharacteristic.

In the modern theory, the characteristic strips of a partial differential equation carry the wave front sets of solutions of a partial differential equation.


[a1] R. Courant, D. Hilbert, "Methods of mathematical physics. Partial differential equations" , 2 , Interscience (1962) (Translated from German)
[a2] L.V. Hörmander, "The analysis of linear partial differential operators" , 1 , Springer (1983)
How to Cite This Entry:
Characteristic strip. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.V. Komlenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article