Dear Colleagues,

Partial differential equations have become a useful tool to describe the natural phenomena of science and engineering. Nonlinear partial differential equations (NLPDEs) arise in many branches of science such as mathematics, physics, mechanics, water waves, computational fluid dynamics, optics, quantum mechanics, shallow water, and engineering.

NLPDEs are widely used to describe physical phenomena in natural science, such as plasma physics, optical fibers, biology, solid-state physics, fluid dynamics, and play a crucial role in research in many disciplines, including in the concept of symmetry. On the other hand, the symmetric properties of NLPDEs are of great importance for the solution of problems in many areas of mathematics. The role of symmetry has also proven to be fundamental in other different disciplines, such as biology, chemistry, and psychology. In this Special Issue, this correlation will be in the foreground. Solutions of NLPDEs play an important role in understanding the mechanisms of many physical phenomena and processes in various areas of natural science. They can help to analyze the stability of these solutions and the movement role of the wave by making graphs of the exact solutions.

Potential themes of interest in this research topic include, but are not limited to, the following:

• Nonlinear partial differential equations;
• Fractional differential equations;
• Soliton wave theory;
• Mathematical methods;
• Stability analysis of dynamical systems;
• Nonlinear water waves;
• Computational fluid dynamics;
• Fiber optics;
• Fractional integral inequalities;
• Computational quantum mechanics;
• Ion-acoustic waves;
• Nonlinear plasma models.

We thus call researchers to contribute to this new Special Issue of the journal Symmetry, titled “Symmetry and Its Applications in Partial Differential Equations”, via the MDPI submission system. We look forward to receiving your contributions of review and original research articles that deal with recent topics and advances in partial differential equations and symmetry. The published papers in this Special Issue of Symmetry could provide crucial examples and new possible research directions for further advancements.

Dr. Mujahid Iqbal
Prof. Dr. Dianchen Lu
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.

• partial differential equations
• mathematical methods
• exact solutions
• solitons
• solitary waves
• analytical and numerical wave solutions