BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Paper detail

Coding of nonlinear states for the Gross-Pitaevskii equation with periodic potential

We study nonlinear states for NLS-type equation with additional periodic potential U(x) (called the Gross-Pitaevskii equation, GPE, in theory of Bose-Einstein Condensate, (BEC)). We prove that if the nonlinearity is defocusing (repulsive, in BEC context) then under certain conditions there exists a homeomorphism between the set of nonlinear states for GPE (i.e. real bounded solutions of some nonlinear ODE) and the set of bi-infinite sequences of numbers from 1 to N for some integer N. These sequences can be viewed as codes of the nonlinear states. Sufficient conditions for the homeomorphism to exist are given in the form of three hypotheses. For a given U(x), the verification of the hypotheses should be done numerically. We report on numerical results for the case of GPE with cosine potential and describe regions in the plane of parameters where this coding is possible.

preprint2012arXivOpen access
Georgy L. AlfimovAlexei I. Avramenko
math-phmath.MPnlin.PSnlin.CDcond-mat.quant-gas
Open graphReviewsDiscussion

Signal facts

What is known right now

Open access2 authors5 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

Next steps

Decide what to do with this paper

Like0Dislike0Score 0

Use like or dislike for the fast social read. The more specific scholarly feedback stays available below when needed.

Save to reading list0
Log in to curate

Reading frame

Keep the important context close to the paper

Keep the important signals around this paper in one place: votes, save state, collection context, reviews and the metadata you need before deciding what to do next.

Authors

Georgy L. AlfimovAlexei I. Avramenko

Institutions

No institution affiliation has been imported for this paper yet.

Add specific reaction

Move through the context

Research map

Open full explorer

Move through nearby people, institutions, topics and adjacent work without leaving the paper page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Structured reviews

0 review(s)

ContributeLeave structured feedbackUse the review template when you have a concrete strength, concern or method question.Open review form
Log in to review

No structured reviews yet. High-signal critique starts here.

Work discussion

0 comment(s)

DiscussAdd a high-signal commentKeep quick notes, caveats and replication pointers separate from formal reviews.Open comment form
Log in to comment

No discussion yet. The first strong comment sets the tone.