Communications in Information and Systems
Volume 13 (2013)
Special Issue in Honor of Marshall Slemrod: Part 3 of 4
Constructing completely integrable fields by a generalized-streamlines method
Pages: 327 – 355
The classical approach to visualizing a flow, in terms of its streamlines, motivates a topological/soft-analytic argument for constrained variational equations. In its full generality, that argument provides an explicit formula for completely integrable solutions to a broad class of $n$-dimensional quasilinear exterior systems. In particular, it yields explicit solutions for extremal surfaces in Minkowski space and for Born-Infeld models.
Hodge-Frobenius equation, Born-Infeld model, completely integrable system, quasilinear system, elliptic-hyperbolic equation
2010 Mathematics Subject Classification