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Abstract
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two particular configurations of the Discrete SelfTrapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this NearToda lattice. The NearToda lattice is then generalized to include singular boundary terms, while at the same time retaining the integrability. When quantizing products of momentum p and position q an ambiguity arises. This is discussed in detail and the need for choosing a particular ordering is shown. The Symmetric Ordering rule, which is equivalent to Weyl's rule, is considered in detail. Explicit formulae for quantizing arbitrary functions of p and q are derived. When the basis functions are chosen as eigenfunctions of the harmonic oscillator, explicit formulae are obtained for the matrix elements of the Hamiltonian. Properties of the solutions to the radially symmetric twodimensional defocusing Nonlinear Schroedinger (NLS) equation are studied analytically and numerically. It is found that no bound states exist. When the initial condition is a dark ring on a background of finite amplitude, the ring initially shrinks until the curvature effects become dominant, forcing the ring to expand to infinity with constant velocity.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  120 
Publication status  Published  1995 
Series  IMMPHD199514 

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Dive into the research topics of 'Nonlinear Hamiltonian systems'. Together they form a unique fingerprint.Projects
 1 Finished

Klassisk og kvantemekanisk behandling af lokalisering, blowup og kaos i ikkelineære systemer
Jørgensen, M. F., Christiansen, P. L., Scott, A. C. & Sørensen, M. P.
01/08/1992 → 18/09/1995
Project: PhD