Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation
Loading...
Date
2014-10-20
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We rigorously analyze the bifurcation of so called nonlinear Bloch waves (NLBs)
from the spectrum in the Gross-Pitaevskii (GP) equation with a periodic potential, in arbitrary
space dimensions. These are solutions which can be expressed as finite sums of
quasi-periodic functions, and which in a formal asymptotic expansion are obtained from solutions
of the so called algebraic coupled mode equations. Here we justify this expansion by
proving the existence of NLBs and estimating the error of the formal asymptotics. The analysis
is illustrated by numerical bifurcation diagrams, mostly in 2D. In addition, we illustrate
some relations of NLBs to other classes of solutions of the GP equation, in particular to so
called out{of{gap solitons and truncated NLBs.
Description
Table of contents
Keywords
mathematical physics