Symmetries of Partial Differential Equations

Dear Colleagues,

This Special Issue of Symmetry is devoted to recent developments in the theory of symmetries and conservation laws for systems of partial differential equations and its applications. The study of symmetries of differential equations has a long history with several innovative landmarks, among the most important of which is the investigation carried out in the nineteenth century by Sophus Lie of continuous groups of transformations which leave differential equations invariant. The accumulated contributions of Lie and other pioneers is now usually referred to as “symmetry analysis of differential equations”. Symmetry analysis is one of the systematic and accurate ways to obtain solutions of differential equations. This powerful technique is commonly used to explore the properties of physical systems, their symmetry structure, invariants, and other qualitative and quantitative features. Conservation laws for differential equations can be found using symmetry analysis, which can also be used to find the exact solutions. Symmetries are also important in verifying and developing numerical schemes. Innovations in symmetry analysis are in constant development and are very useful, especially in the theory of the integrability of nonlinear dynamical systems. We cordially invite all authors to submit relevant articles to this Special Issue.

The topics of interest for this Special Issue include but are not limited to:

1. Symmetries and conservation laws;
2. Exactly and completely integrable nonlinear dynamical systems;
3. Point symmetries of partial differential equations;
4. Potential symmetries of partial differential equations;
5. Integrable reductions;
6. Symmetry groups of partial differential equations.

Prof. Dr. Denis Blackmore
Dr. Yarema Prykarpatsky
Guest Editors

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. 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 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.

• symmetries
• conservation laws
• partial differential equations
• reductions
• integrability
• dynamical systems