Lie Symmetry, Nonlinear Partial Differential Equations and Geometry

Dear Colleagues,

Lie symmetry analysis is a powerful tool for studying nonlinear partial differential equations, enabling the construction of invariant solutions and conservation laws through continuous transformation groups that leave differential equations invariant. Rooted in the work of Sophus Lie, the theory provides a systematic framework for analyzing nonlinear PDEs, particularly those arising in geometry.

Many fundamental problems in differential geometry—such as curvature, geodesics, minimal surfaces, and geometric flows—are governed by nonlinear PDEs that naturally admit geometric symmetries, including translations, rotations, scalings, and re-parametrizations. This Special Issue invites contributions highlighting the role of Lie symmetry analysis in nonlinear PDEs, with emphasis on their geometric structure and applications.

Prof. Dr. Fiazuddin Zaman
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 250 words) can be sent to the Editorial Office for assessment.

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.