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Ricerche di Matematica

, Volume 68, Issue 2, pp 503–512 | Cite as

The Gross–Pitaevskii equation: Bäcklund transformations and admitted solutions

  • Sandra CarilloEmail author
  • Federico Zullo
Article

Abstract

Bäcklund transformations are applied to study the Gross–Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwarzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross–Pitaevskii equation are obtained.

Keywords

Nonlinear ordinary differential equations Gross–Pitaevskii equation Bäcklund transformations Schwarzian derivative 

Mathematics Subject Classification

35A24 49K15 37K35 35Q55 

Notes

Acknowledgements

The financial support of GNFM-INdAM, INFN, Sapienza Università di Roma and Unversità di Brescia are gratefully acknowledged.

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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Dipartimento Scienze di Base e Applicate per l’IngegneriaSapienza Università di RomaRomeItaly
  2. 2.I.N.F.N. - Sezione Roma1 Gr. IV - Mathematical Methods in NonLinear PhysicsRomeItaly
  3. 3.DICATAM, Universitá di BresciaBresciaItaly

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