Graduate Thesis Or Dissertation
 

The local conservation laws of the nonlinear Schrödinger equation

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  • The nonlinear Schrödinger equation is a well-known partial differential equation that provides a successful model in nonlinear optic theory, as well as other applications. In this dissertation, following a survey of mathematical literature, the geometric theory of differential equations is applied to the nonlinear Schrödinger equation. The main result of this dissertation is that the known list of local conservation laws for the nonlinear Schrödinger equation is complete. A theorem is proved and used to produce a sequence of local conservation law characteristics of the nonlinear Schrödinger equation. The list of local conservation laws as given by Faddeev and Takhtajan and a theorem of Olver, which provides a one-to-one correspondence between equivalence classes of conservation laws and equivalence classes of their characteristics, are then used to prove the main result.
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