Symmetries and conservation laws of high-order systems of partial differential equations
Date
2011-07-07
Authors
Morris, R. M.
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Abstract
Conservation laws for nonlinear partial di erential equations (pdes) have been
determined through di erent approaches. In this dissertation, we study conservation
laws for some third-order systems of pdes, viz., some versions of the
Boussinesq equations, as well as a version of the BBM equation and the wellknown
Ito equation. It is shown that new and interesting conserved quantities
arise from `multipliers' that are of order greater than one in derivatives of the
dependent variables. Furthermore, the invariance properties of the conserved
ows with respect to the Lie point symmetry generators are investigated via
the symmetry action on the multipliers.