DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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The Lagrange–Charpit characteristic system

Definition

For $F \in C^{2} (O)$ on $O \subseteq R^{n} \times R \times R^{n}$ , the Lagrange–Charpit system is

$\dot{X} = F_{p}, \dot{Z} = P \cdot F_{p}, \dot{P} = - F_{x} - P F_{z},$

with all derivatives evaluated at $(X, Z, P)$ . The alternative contact normalization $\dot{Z} = P \cdot F_{p} - F$ agrees with this one only along $F = 0$ ; it is not silently substituted off that constraint.

Depends on

Fully nonlinear first-order PDEs and complete integrals

Used by

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Part I: Explicit methods — Lecture notes for MA342H (standard reference, not scraped)