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Axioms
Special Issues
Nonlinear Schrödinger Equations
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Nonlinear Schrödinger Equations

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 1413

Special Issue Editor

Prof. Dr. Pascal Bégout

E-Mail Website
Guest Editor
Institut de Mathématiques de Toulouse, Toulouse School of Economics, Toulouse, France
Interests: qualitative properties of solutions to nonlinear Schrödinger equations; asymptotic behaviour; existence; uniqueness; finite time extinction

Special Issue Information

Dear Colleagues,

Schrödinger equations (linear and nonlinear) have been of great interest to mathematicians around the world for more than 40 years now. For this Special Issue, we are interested by innovative results concerning these equations. The scope of this Special Issue covers both theoretical and numerical results such as existence and uniqueness, blow-up, asymptotic behaviour, study of solitons, bound (or ground) state of solutions, self-similar solutions and numerical analysis and simulations.

Prof. Dr. Pascal Bégout
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear Schrödinger equations
  • asymptotic behaviour
  • blow-up
  • existence
  • uniqueness and non-uniqueness
  • smoothness
  • self-similar solutions
  • solitons
  • stability
  • numerical analysis
  • numerical simulations

Published Papers (1 paper)

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Research

25 pages, 11760 KiB  
Article
Regular, Beating and Dilogarithmic Breathers in Biased Photorefractive Crystals
by Carlos Alberto Betancur-Silvera, Aurea Espinosa-Cerón, Boris A. Malomed and Jorge Fujioka
Axioms 2024, 13(5), 338; https://doi.org/10.3390/axioms13050338 - 20 May 2024
Viewed by 480
Abstract
The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schrödinger equation (GNLSE). We use a variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystals, finding that the VA equations [...] Read more.
The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schrödinger equation (GNLSE). We use a variational approximation (VA) to predict the propagation of solitary-wave inputs in the crystals, finding that the VA equations involve a dilogarithm special function. The VA predicts that solitons and breathers exist, and the Vakhitov–Kolokolov criterion predicts that the solitons are stable solutions. Direct simulations of the underlying GNLSE corroborates the existence of such stable modes. The numerical solutions produce both regular breathers and ones featuring beats (long-period modulations of fast oscillations). In the latter case, the Fourier transform of amplitude oscillations reveals a nearly discrete spectrum characterizing the beats dynamics. Numerical solutions of another type demonstrate the spontaneous splitting of the input pulse in two or several secondary ones. Full article
(This article belongs to the Special Issue Nonlinear Schrödinger Equations)
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