Now showing items 1-4 of 4
Rigorous numerics for NLS: Bound states, spectra, and controllability
(Physica D: Nonlinear Phenomena, 2015-12-31)
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound-state solutions and establishing certain spectral ...
Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates
(SIAM Journal on Numerical Analysis, 2013-12-31)
We present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential ...
Rigorous numerics in floquet theory: Computing stable and unstable bundles of periodic orbits
(SIAM Journal on Applied Dynamical Systems, 2013-12-31)
In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of nonautonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental ...
Existence of secondary bifurcations or isolas for PDEs
(Nonlinear Analysis, Theory, Methods and Applications, 2011-12-31)
In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ...