Special Issue "Ordinary and Partial Differential Equations: Theory and Applications"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 December 2019.

Special Issue Editor

Guest Editor
Prof. Clemente Cesarano Website E-Mail
Section of Mathematics – International Telematic University UNINETTUNO
Phone: +39.0669207675
Interests: special functions; orthogonal polynomials; fractional calculus; numerical methods; ODE and PDE

Special Issue Information

Dear Colleagues,

The study of differential equations is useful for understanding natural phenomena. In this Special Issue, we aim to present the latest research on the properties of ODE (Ordinary Differential Equations) and PDE (Partial Differential Equations) related to different techniques for finding solutions and methods describing the nature of these solutions or their related approximations.

In addition, we welcome papers on numerical aspects using classical or non-standard approaches, for example, the concepts and related formalism of special functions. Furthermore, articles on fractional differential equations are of interest, as are contributions related to the symmetry approach to problems of integrability in the field of differential equations.

Prof. Clemente Cesarano
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 papers will be 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. Symmetry 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 1400 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

  • symmetries
  • ODE
  • PDE
  • numerical methods
  • fractional calculus

Published Papers (1 paper)

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Research

Open AccessArticle
N-Soliton Solutions for the NLS-Like Equation and Perturbation Theory Based on the Riemann–Hilbert Problem
Symmetry 2019, 11(6), 826; https://doi.org/10.3390/sym11060826 - 22 Jun 2019
Cited by 2
Abstract
In this paper, a kind of nonlinear Schrödinger (NLS) equation, called an NLS-like equation, is Riemann–Hilbert investigated. We construct a 2 × 2 Lax pair associated with the NLS equation and combine the spectral analysis to formulate the Riemann–Hilbert (R–H) problem. Then, we [...] Read more.
In this paper, a kind of nonlinear Schrödinger (NLS) equation, called an NLS-like equation, is Riemann–Hilbert investigated. We construct a 2 × 2 Lax pair associated with the NLS equation and combine the spectral analysis to formulate the Riemann–Hilbert (R–H) problem. Then, we mainly use the symmetry relationship of potential matrix Q to analyze the zeros of det P + and det P ; the N-soliton solutions of the NLS-like equation are expressed explicitly by a particular R–H problem with an unit jump matrix. In addition, the single-soliton solution and collisions of two solitons are analyzed, and the dynamic behaviors of the single-soliton solution and two-soliton solutions are shown graphically. Furthermore, on the basis of the R–H problem, the evolution equation of the R–H data with the perturbation is derived. Full article
(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications)
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