QA193 : Lie Superposition Principle with Applications in Partial Differential Equations
Thesis > Central Library of Shahrood University > Mathematical Sciences > MSc > 2013
Authors:
Abstarct: In this thesis a rigorous geometric proof of the Lie’s Theorem on nonlinear superposition
rules for solutions of non-autonomous ordinary differential equations is given filling in all
gaps present in the existing literature. The proof is baxsed on an alternative but equivalent
definition of a superposition rule: it is considered as a foliation with some suitable properties.
The problem of uniqueness of the superposition function is solved, the key point being the
codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as
a more convincing argument supporting the use of this alternative definition of superposition
rule, it is shown that this definition allows an immediate generalization of Lie’s Theorem for
the case of systems of partial differential equations.
Keywords:
#differential equation #nonlinear superposition #lie systems #lie algebra #vector field #foliation Link
Keeping place: Central Library of Shahrood University
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Keeping place: Central Library of Shahrood University
Visitor: