2,536 research outputs found
Periodic Quasi - Exactly Solvable Models
Various quasi-exact solvability conditions, involving the parameters of the
periodic associated Lam{\'e} potential, are shown to emerge naturally in the
quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity
of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible
for the surprisingly large number of allowed solvability conditions in the
associated Lam{\'e} case. We also study the singularity structure of the
quantum momentum function, which yields the band edge eigenvalues and
eigenfunctions.Comment: 11 pages, 5 table
Controllability distributions and systems approximations: a geometric approach
Given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a Taylor series approximation of it. The value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. The relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximatio
Boundary effects on localized structures in spatially extended systems
We present a general method of analyzing the influence of finite size and
boundary effects on the dynamics of localized solutions of non-linear spatially
extended systems. The dynamics of localized structures in infinite systems
involve solvability conditions that require projection onto a Goldstone mode.
Our method works by extending the solvability conditions to finite sized
systems, by incorporating the finite sized modifications of the Goldstone mode
and associated nonzero eigenvalue. We apply this method to the special case of
non-equilibrium domain walls under the influence of Dirichlet boundary
conditions in a parametrically forced complex Ginzburg Landau equation, where
we examine exotic nonuniform domain wall motion due to the influence of
boundary conditions.Comment: 9 pages, 5 figures, submitted to Physical Review
Controllability distributions and systems approximations: a geometric approach
Given a nonlinear system, a relation between controllability distributions defined for a nonlinear system and a Taylor series approximation of it is determined. Special attention is given to this relation at the equilibrium. It is known from nonlinear control theory that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant (controllability) distributions. By dealing with a k-th Taylor series approximation of the system, the authors are able to decide when the solvability conditions of these kinds of problem are equivalent for the nonlinear system and its approximation. Some cases when the solution obtained from the approximated system is an approximation of an exact solution for the original problem are distinguished. Some examples illustrate the result
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